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The Ultimate Guide to Time-Series Analysis (With Examples and Applications)

What is time-series analysis.

Time-series analysis is a statistical technique that deals with time-series data or trend analysis. It involves the identification of patterns, trends, seasonality, and irregularities in the data observed over different periods. This method is particularly useful for understanding the underlying structure and pattern of the data.

When performing time-series analysis, you will use a mathematical set of tools to look into time-series data and learn not only what happened but also when and why it happened.

Time-series analysis vs. time-series forecasting

While both time-series analysis and time-series forecasting are powerful tools that developers can harness to glean insights from data over time, they each have specific strengths, limitations, and applications.

Time-series analysis isn't about predicting the future; instead, it's about understanding the past. It allows developers to decompose data into its constituent parts—trend, seasonality, and residual components. This can help identify any anomalies or shifts in the pattern over time.

Key methodologies

Key methodologies used in time-series analysis include moving averages, exponential smoothing, and decomposition methods. Methods such as Autoregressive Integrated Moving Average (ARIMA) models also fall under this category—but more on that later.

On the other hand, time-series forecasting uses historical data to predict future events. The objective here is to build a model that captures the underlying patterns and structures in the time-series data to predict future values of the series.

Checklist for Time-Series Analysis

When analyzing time-series data, a structured approach not only simplifies the process but also enhances the accuracy and relevance of your outcomes. Below is a comprehensive checklist to guide your analysis, ensuring that no critical component is overlooked.

Look for trends: At the heart of time series analysis is the identification of trends over a period, typically through rolling aggregates that smooth out short-term fluctuations to reveal a long-term trend.

Check for seasonality: Seasonality captures the repetitive and cyclical patterns in your data, occurring at regular intervals. Identifying these patterns is vital as they offer insights into predictable changes. Integrating your contextual knowledge about the dataset can greatly aid in making sense of these seasonal behaviors.

Once you've identified the trends and seasonality within your data, the next step is to construct a model that combines these elements. This model should roughly match the underlying data, providing a more accurate representation of the observed behaviors.

Attempt a model of remaining noise: After accounting for trend and seasonality, the “noise” remains—the part of the data not explained by the model. Analyze this noise by taking your data modulo trend and seasonality to inspect its behavior. Ideally, it should exhibit a stationary distribution, meaning it appears somewhat chaotic but has a stable average and variance over time.

With a stationary noise distribution, you can apply statistical heuristics, such as calculating the average and variance, to make future projections. These estimates can serve as a basis for more complex forecasting. For a more detailed analysis, you might explore stochastic models like Brownian motion . These models account for randomness and can provide more nuanced insights into how your time series data might evolve.

Integrating your understanding of the data’s context is crucial throughout each step of your analysis. Whether industry-specific knowledge or familiarity with specific patterns, this insight will help refine your models and projections, leading to more accurate and meaningful models.

‌‌Use Cases for Time-Series Analysis

The “time” element in time-series data means that the data is ordered by time. Time series data refers to a sequence of data points or observations recorded at specific intervals. This data type is commonly used to analyze trends, patterns, and behaviors over time. Check out our earlier blog post to learn more and see examples of time-series data .

A typical example of time-series data is stock prices or a stock market index. However, even if you’re not into financial and algorithmic trading, you probably interact daily with time-series data.

Here are some other examples of time-series data for time-series analysis:

• IoT and sensor data : Monitoring and analyzing sensor data from devices, machinery, or infrastructure to predict maintenance needs, optimize performance, and detect anomalies.
• Weather forecasting : Utilizing historical weather data to forecast future meteorological conditions, such as temperature, precipitation, and wind patterns.
• E-commerce and retail : Tracking sales data over time to identify seasonal trends, forecast demand, and optimize inventory management and pricing strategies.
• Healthcare : Analyzing patient vital signs, medical records, and treatment outcomes to improve healthcare delivery, disease surveillance, and patient care.
• Energy consumption : Studying electricity or energy usage patterns to optimize consumption, forecast demand, and support energy efficiency initiatives.
• Manufacturing and supply chain : Monitoring production processes, inventory levels, and supply chain data to enhance operational efficiency and demand forecasting.
• Web traffic and user behavior : Analyzing website traffic, user engagement metrics, and customer behavior patterns to enhance digital marketing strategies and user experience.

As you can see, time-series data is part of many of your daily interactions, whether you're driving your car through a digital toll, receiving smartphone notifications about the weather forecast, or suggesting you should walk more. If you're working with observability, monitoring different systems to track their performance and ensure they run smoothly, you're also working with time-series data. And if you have a website where you track customer or user interactions (event data), guess what? You're also a time-series analysis use case.

To illustrate this in more detail, let’s look at the example of health apps—we'll refer back to this example throughout this blog post.

A Real-World Example of Time-Series Analysis

If you open a health app on your phone, you will see all sorts of categories, from step count to noise level or heart rate. By clicking “show all data” in any of these categories, you will get an almost endless scroll (depending on when you bought the phone) of step counts, timestamped with the sampling time. ‌‌

This data is the raw foundation of the step count time series. Remember, this is just one of many parameters your smartphone or smartwatch samples. While many parameters don’t mean much to most people (yes, I’m looking at you, heart rate variability), when combined with other data, these parameters can estimate overall quantifiers, such as cardio fitness. ‌‌

To achieve this, you need to connect the time-series data into one large dataset with two identifying variables—time and type of measurement. This is called panel data . Separating it by type gives you multiple time series, while picking one particular point in time gives you a snapshot of everything about your health at a specific moment, like what was happening at 7:45 a.m.

Why Should You Use Time-Series Analysis?

Now that you’re more familiar with time-series data, you may wonder what to do with it and why you should care. So far, we’ve mostly just been reading off data—how many steps did I take yesterday? Is my heart rate okay?

But time-series analysis can help us answer more complex or future-related questions, such as forecasting. When did I stop walking and catch the bus yesterday? Is exercise making my heart stronger?

To answer these, we need more than just reading the step counter at 7:45 a.m.—we need time-series analysis. Time-series analysis happens when we consider part or the entire time series to see the “bigger picture.” We can do this manually in straightforward cases: for example, by looking at the graph that shows the days when you took more than 10,000 steps this month. ‌‌

But if you wanted to know how often this occurs or on which days, that would be significantly more tedious to do by hand. Very quickly, we bump into problems that are too complex to tackle without using a computer, and once we have opened that door, a seemingly endless stream of opportunities emerges. We can analyze everything, from ourselves to our business, and make them far more efficient and productive than ever.

T‌‌he four components of time-series analysis

To correctly analyze time-series data, we need to look at the four components of a time series:

• Trend : this is a long-term movement of the time series, such as the decreasing average heart rate of workouts as a person gets fitter.
• Seasonality : regular periodic occurrences within a time interval smaller than a year (e.g., higher step count in spring and autumn because it’s not too cold or too hot for long walks).
• Cyclicity : repeated fluctuations happened that are longer in duration than irregularities but shorter than what would constitute a trend. In our walking example, this would be a one-week sightseeing holiday every four to five months.
• Irregularity : short-term irregular fluctuations or noise, such as a gap in the sampling of the pedometer or an active team-building day during the workweek.

Let’s go back to our health app example. One thing you may see immediately, just by looking at a time-series analysis chart, is whether your stats are trending upward or downward. That indicates whether your stats are generally improving or not. By ignoring the short-term variations, it's easier to see if the values rise or decline within a given time range. This is the first of the four components of a time series—trend.

‌‌Types of Time-Series Analysis

Time to dive deeper into how time-series analysis can extract information from time-series data. To do this, let’s divide time-series analysis into five distinct types.

Exploratory analysis

Exploratory analysis is helpful when describing what you see and explaining why you see it in a given time series. It essentially entails decomposing the data into trend, seasonality, cyclicity, and irregularities. ‌‌

Once we decompose the series, we can explain what each component represents in the real world and, perhaps, what caused it. This task is not as easy as it may seem and often involves spectral decomposition to find any specific frequencies of recurrences and autocorrelation analysis to see if current values depend on past values.

Curve fitting

Since time series is a discrete set, you can always tell exactly how many data points it contains. But what if you want to know the value of your time-series parameter at a point in time that is not covered by your data? ‌‌

To answer this question, we must supplement our data with a continuous set—a curve. You can do this in several ways, including interpolation and regression. The former is an exact match for parts of the given time series and is primarily useful for estimating missing data points. On the other hand, the latter is a “best-fit” curve, where you have to make an educated guess about the form of the function to be fitted (e.g., linear) and then vary the parameters until your best-fit criteria are satisfied. ‌‌

What constitutes a “best-fit” situation depends on the desired outcome and problem. Using regression analysis, you also obtain the best-fit function parameters that can have real-world meaning, for example, post-run heart rate recovery as an exponential decay fit parameter. In regression, we get a function that describes the best fit to our data even beyond the last record opening the door to extrapolation predictions.

Forecasting

Statistical inference is the process of generalization from sample to whole. It can be done over time in time-series data, giving way to future predictions or forecasting: from extrapolating regression models to more advanced techniques using stochastic simulations and machine learning. If you want to know more, check out our article about time-series forecasting .

Classification and segmentation

Time-series classification is identifying the categories or classes of an outcome variable based on time-series data. In other words, it's about associating each time-series data with one label or class.

For instance, you might use time-series classification to categorize server performance into 'Normal' or 'Abnormal' based on CPU usage data collected over time. The goal is to create a model to accurately predict the class of new, unseen time-series data.

Classification models commonly used include decision trees, nearest neighbor classifiers, and deep learning models. These models can handle the temporal dependencies in time-series data, making them ideal for this task.

Time-series segmentation , on the other hand, involves breaking down a time series into segments, each representing a specific event or state. The objective is to simplify the time-series data by representing it as a sequence of more manageable segments.

For example, in analyzing website traffic data, you might segment the data into periods of 'High,' 'Medium,' and 'Low' activity. This segmentation can provide simpler, more interpretable insights into your data.

Segmentation methods can be either top-down, where the entire series is divided into segments, or bottom-up, where individual data points are merged into segments. Each method has its strengths and weaknesses, and the choice depends on the nature of your data and your specific requirements.

As you may have already guessed, problems rarely require just one type of analysis. Still, it is crucial to understand the various types to appreciate each aspect of the problem correctly and formulate a good strategy for addressing it.

Time-Series Analysis Visualization and Examples

There are many ways to visualize a time series and certain types of analysis. A run chart is the most common choice for simple time series with one parameter, essentially just data points connected by lines. ‌‌

However, there are usually several parameters you would like to visualize at once. You have two options in this case: overlapping or separated charts. Overlapping charts display multiple series on a single pane, whereas separated charts show individual series in smaller, stacked, and aligned charts, as seen below.

Let’s take a look at three different real-world examples illustrating what we’ve learned so far. To keep things simple and best demonstrate the analysis types, the following examples will be single-parameter series visualized by run charts.

Electricity demand in Australia

Stepping away from our health theme, let's explore the time series of Australian monthly electricity demand in the figures below. Visually, it is immediately apparent there is a positive trend, as one would expect with population growth and technological advancement. ‌‌

Second, the data has a pronounced seasonality, as demand in winter will not be the same as in summer. An autocorrelation analysis can help us understand this better. Fundamentally, this checks the correlation between two points separated by a time delay or lag. ‌‌

As we can see in the autocorrelation function (ACF) graph, the highest correlation occurs with a delay of exactly 12 months (implying a yearly seasonality) and the lowest with a half-year separation since electricity consumption is highly dependent on the time of year (air conditioning, daylight hours, etc.). ‌‌

Since the underlying data has a trend (it isn’t stationary), the ACF dies down as the lag increases since the two points are further and further apart, with the positive trend separating them more each year. These conclusions can become increasingly non-trivial when data spans less intuitive variables.

Boston Marathon winning times

Back to our health theme from the more exploratory previous example, let’s look at the winning times of the Boston Marathon. The aim here is different: we don’t particularly care why the winning times are such. We want to know whether they have been trending and where we can expect them to go. ‌‌

To do this, we need to fit a curve and assess its predictions. But how do you know which curve to choose? There is no universal answer to this; however, even visually, you can eliminate a lot of options. The figure below shows you four different choices of fitted curves:‌‌

‌‌‌‌1. A linear fit

f(t) = at + b

‌‌2. A piecewise linear fit, which is just several linear fit segments spliced together

3. An exponential fit

f(t) = ae bt + c ‌

4. A cubic spline fit that’s like a piecewise linear fit where the segments are cubic polynomials with smooth joins

f(t) = at 3 + bt 2 + ct + d

‌‌Looking at the graph, it’s clear that the linear and exponential options aren’t a good fit. It boils down to the cubic spline and the piecewise linear fits. In fact, both are useful, although for different questions. ‌‌

The cubic spline is visually the best historical fit, but in the future (purple section), it trends upward in an intuitively unrealistic way, with the piecewise linear producing a far more reasonable prediction. Therefore, one has to be very careful when using good historical fits for prediction; understanding the underlying data is extremely important when choosing forecasting models.

Electrocardiogram analysis

As a final example to illustrate the classification and segmentation types of problems, take a look at the following graph. Imagine wanting to train a machine to recognize certain heart irregularities from electrocardiogram (ECG) readings. ‌‌

First, this is a segmentation problem, as you need to split each ECG time series into sequences corresponding to one heartbeat cycle. The dashed red lines in the diagram are the splittings of these cycles. Having done this on both regular and irregular readings, this becomes a classification problem—the algorithm should now analyze other ECG readouts and search for patterns corresponding to either a regular or irregular heartbeat.

‌ Learn More About Time-Series Analysis

This was just a glimpse of what time-series analysis offers. By now, you should know that time-series data is ubiquitous. To measure the constant change around you for added efficiency and productivity (whether in life or business), you need to go for it and start analyzing it .‌‌

I hope this article has piqued your interest, but nothing compares to trying it out yourself. And for that, you need a robust database to handle the massive time-series datasets. Try Timescale , a modern, cloud-native relational database platform for time series that will give you reliability, fast queries, and the ability to scale infinitely to understand better what is changing, why, and when .‌‌

Continue your time-series journey:

• What Is Time-Series Data? (With Examples)
• What Is Time-Series Forecasting?
• Time-Series Database: An Explainer
• A Guide on Data Analysis on PostgreSQL
• What Is a Time-Series Graph With Examples
• What Is a Time-Series Plot, and How Can You Create One
• Get Started With TimescaleDB With Our Tutorials
• How to Write Better Queries for Time-Series Data Analysis With Custom SQL Functions
• Speeding Up Data Analysis With TimescaleDB and PostgreSQL
• Clay Grewcoe

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Time series analysis: what it is and what it does

Most marketing research is cross-sectional but time series analysis is an often-overlooked but valuable tool. This article offers an overview of univariate analysis, causal modeling, multiple time series and more.

Editor's note: Kevin Gray is president of Cannon Gray LLC, a marketing science and analytics consultancy. This article appeared in the September 23, 2013, edition of Quirk's e-newsletter.

Most marketing research is cross-sectional, meaning our data represent one slice in time. However, we also have data collected over many periods, such as weekly sales data for our brands and competitors' brands. This is an example of time series data. Time series analysis is a specialized area of statistics to which many marketing researchers have had limited exposure, despite it having many important applications in MR.

Why is the distinction between cross-sectional and time series analysis important? For several reasons - one being that research objectives are usually different. Another is that most of the statistical methods we learn in college and use in marketing research are intended for cross-sectional data and if we apply them to time series data, results may be misleading. Time is a dimension in the data we need to take into account.

Time series analysis is a complex topic but to put it simply, when we use our usual cross-sectional techniques (e.g., regression) on time series data, one or more of the following outcomes can occur.

• Standard errors can be far off. More often than not, p-values will be too small and variables can appear more significant than they really are.
• Regression coefficients can be seriously biased.
• We do not maximize the information provided by the serial correlation in the data.

Table 1 shows a simple illustration of what a time series data file looks like. The column labeled "Date" is the date variable and corresponds to a respondent ID in survey research data. "Week," the sequence number of each week, is included because using it (rather than actual date) reduces graph clutter. The sequence number can also serve as a trend variable in certain time series models. In this illustration, "Sales" are the number of units sold each week.

Gordon Scott has been an active investor and technical analyst or 20+ years. He is a Chartered Market Technician (CMT).

Investopedia / Crea Taylor

A time series is a sequence of data points that occur in successive order over some period of time. This can be contrasted with cross-sectional data , which captures a point in time.

In investing, a time series tracks the movement of the chosen data points, such as a security’s price, over a specified period of time with data points recorded at regular intervals. There is no minimum or maximum amount of time that must be included, allowing the data to be gathered in a way that provides the information being sought by the investor or analyst examining the activity.

Key Takeaways

• A time series is a data set that tracks a sample over time.
• In particular, a time series allows one to see what factors influence certain variables from period to period.
• Time series analysis can be useful to see how a given asset, security, or economic variable changes over time.
• Forecasting methods using time series are used in both fundamental and technical analysis.
• Although cross-sectional data is seen as the opposite of time series, the two are often used together in practice.

A time series can be taken on any variable that changes over time. In investing, it is common to use a time series to track the price of a security over time. This can be tracked over the short term, such as the price of a security on the hour over the course of a business day, or the long term, such as the price of a security at close on the last day of every month over the course of five years.

Time series analysis can be useful to see how a given asset, security, or economic variable changes over time. It also can be used to examine how the changes associated with the chosen data point compare to shifts in other variables over the same time period.

Time series is also used in several nonfinancial contexts, such as measuring the change in population over time. The figure below depicts such a time series for the growth of the U.S. population over the century from 1900 to 2000.

C.K. Taylor

Suppose you wanted to analyze a time series of daily closing stock prices for a given stock over a period of one year. You would obtain a list of all the closing prices for the stock from each day for the past year and list them in chronological order. This would be a one-year daily closing price time series for the stock.

Delving a bit deeper, you might analyze time series data with technical analysis tools to know whether the stock’s time series shows any seasonality. This will help to determine if the stock goes through peaks and troughs at regular times each year. Analysis in this area would require taking the observed prices and correlating them to a chosen season. This can include traditional calendar seasons, such as summer and winter, or retail seasons, such as holiday seasons.

Alternatively, you can record a stock’s share price changes as it relates to an economic variable, such as the unemployment rate . By correlating the data points with information relating to the selected economic variable, you can observe patterns in situations exhibiting dependency between the data points and the chosen variable.

One potential issue with time series data is that since each variable is dependent on its prior state or value, there can be a great deal of autocorrelation , which can bias results.

Time series forecasting uses information regarding historical values and associated patterns to predict future activity. Most often, this relates to trend analysis, cyclical fluctuation analysis, and issues of seasonality. As with all forecasting methods, success is not guaranteed.

The Box-Jenkins Model , for instance, is a technique designed to forecast data ranges based on inputs from a specified time series. It forecasts data using three principles: autoregression , differencing, and moving averages . These three principles are known as p, d, and q, respectively. Each principle is used in the Box-Jenkins analysis, and together they are collectively shown as an autoregressive integrated moving average, or ARIMA (p, d, q). ARIMA can be used, for instance, to forecast stock prices or earnings growth.

Another method, known as rescaled range analysis , can be used to detect and evaluate the amount of persistence, randomness, or  mean reversion  in time series data. The rescaled range can be used to extrapolate a future value or average for the data to see if a trend is stable or likely to reverse.

Cross-Sectional vs. Time Series Analysis

Cross-sectional analysis is one of the two overarching comparison methods for stock analysis. Cross-sectional analysis looks at data collected at a single point in time, rather than over a period of time. The analysis begins with the establishment of research goals and the definition of the variables that an analyst wants to measure. The next step is to identify the cross section, such as a group of peers or an industry, and to set the specific point in time being assessed. The final step is to conduct analysis, based on the cross section and the variables, and come to a conclusion on the performance of a company or organization. Essentially, cross-sectional analysis shows an investor which company is best given the metrics that they care about.

Time series analysis, known as trend analysis when it applies to technical trading, focuses on a single security over time. In this case, the price is being judged in the context of its past performance. Time series analysis shows an investor whether the company is doing better or worse than before by the measures that they care about. Often these will be classics like  earnings per share (EPS) , debt to equity ,  free cash flow (FCF) , and so on. In practice, investors will usually use a combination of time series analysis and cross-sectional analysis before making a decision—for example, looking at the EPS over time and then checking the industry benchmark EPS.

What Are Some Examples of Time Series?

A time series can be constructed by any data that is measured over time at evenly spaced intervals. Historical stock prices, earnings, gross domestic product (GDP), or other sequences of financial or economic data can be analyzed as a time series.

How Do You Analyze Time Series Data?

Statistical techniques can be used to analyze time series data in two key ways: to generate inferences on how one or more variables affect some variable of interest over time, or to forecast future trends. Unlike cross-sectional data, which is essentially one slice of a time series, the arrow of time allows an analyst to make more plausible causal claims.

What Is the Distinction Between Cross-Sectional and Time Series Data?

A cross section looks at a single point in time, which is useful for comparing and analyzing the effect of different factors on one another or describing a sample. Time series involves repeated sampling of the same data over time. In practice, both forms of analysis are commonly used, and when available, they are used together.

How Are Time Series Used in Data Mining?

Data mining is a process that turns reams of raw data into useful information. By utilizing software to look for patterns in large batches of data, businesses can learn more about their customers to develop more effective marketing strategies, increase sales, and decrease costs. Time series, such as a historical record of corporate filings or financial statements, are particularly useful here to identify trends and patterns that may be forecasted into the future.

A time series is a sequence of numerical data points in successive order. In investing, it tracks the movement of the chosen data points at regular intervals and over a specified period of time. In investing, a time series records chosen data points (such as a security’s price) at regular intervals and tracks their movement over a specified period of time.

Time series analysis can be useful to see what factors influence certain variables from period to period. It can also provide insights into how an asset, security, or economic variable changes over time.

A variety of financial and economic data, such as historical stock prices, earnings, and GDP, can be analyzed as a time series.

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A Complete Guide to Time Series Analysis and Forecasting

It’s one thing to record data and observe how it has changed between one time and another—it’s another to examine how data changes over time and to analyze shifts in data points at concrete time intervals. Time is a critical part of all data analysis, and it can impact conclusions, forecasts, and other recommendations from data scientists.

To accurately understand the relationship between data shifts and time, data analysts need to understand time series analysis and forecasting. This guide will break down what time series analysis is, the role it plays in forecasting efforts, and certain models data analysts use to perform time series analysis.

Use the following clickable menu to skip ahead to any section:

• What is time series analysis?
• How is time series analysis used in data analytics?
• Time series analysis use cases
• Types of time series analysis
• Time series analysis models and techniques
• Final thoughts

Ready to learn more about time series analysis? Let’s get started!

1. What is time series analysis?

Time series analysis is a method of analyzing data points collected over a set time period. Through time series analysis, data analysts measure various data points at regular intervals. In this way, they can see how the points of data change with the passage of time, instead of gathering data points randomly or intermittently.

Time series analysis is important because it doesn’t just show how different variables can change over time. It also shows how data points adjust over the course of the entire measurement time frame—not just between when data collection begins and when it ends.

Time series analysis usually needs many data points. The more data points collected, the more consistent and reliable the results will be. Furthermore, acquiring more data points reduces the chance that any patterns or trends detected are outliers or unreliable.

When used properly, time series data analysis can be utilized to predict future data performance based on past results.

2. How is time series analysis used in data analytics?

Time series data analysis is used in a variety of contexts. Many organizations leverage time series analysis to understand the causes of different systemic patterns or detected trends over time. When used with a graph or other data visualization element , businesses can see things like seasonal trends and determine:

• Why those trends occur,
• Whether they can affect those trends for better results, and
• How the trends may change or stay the same in the future

In fact, that last focus is why most organizations leverage time series analysis in the first place. Through acquiring and analyzing enough data, businesses and other organizations can perform time series forecasting. They can predict the likelihood or possibility of future events.

3. Time series analysis use cases

Let’s take a look at a few use cases or examples of time series analysis in action.

One great example of time series analysis and action is the examination of the stock market. Automated trading algorithms and experienced stock market traders alike both perform time series analyses on stocks, bonds, and other financial vehicles.

They attempt to look at how stocks and other assets change in value over time so they can predict the value of those assets in the future. This is highly complex and is far from 100% reliable; after all, there’s a reason investing in the stock market is never a sure thing.

Still, time series analysis is part of what allows trading algorithms to predict stock market movements with some reliability. Algorithms designed by expert coders are also leveraged in industries such as in healthcare, finance, and so on.

Another good example is meteorology or climatology. Climate specialists look at concrete data points such as sea levels, recorded temperatures, humidity levels, and more. Then they compare those data points to how they have changed over time by collecting the data at the exact same time each week, month, or year.

Through these collection efforts, climate specialists can leverage time series analysis to determine:

• How the weather is changing
• Whether certain effects or others are responsible for changing weather patterns
• How the weather may change or evolve in the future
• … and many other things!

In both of these examples, time series analysis is an important method that data analysts must incorporate into their strategies to understand the full picture.

From large businesses to micro businesses, or businesses with ten employees or fewer (which make up 92% of all businesses in the United States), time series analysis is a vital tool useful for understanding markets, business limitations, finances, and more.

4. Types of time series analysis

Data analysts often use different types of time series analyses rather than constructing overly complex or crowded charts and graphs. Overfitting models or overly complex models may produce a lack of fit or may make it difficult for analysts to distinguish between real relationships and random errors.

To that end, some of the most common times series analysis models include:

• Exploratory analysis models, which highlight and focus on primary features of the time series data in visual formats
• Classification models, which both identify and assign categories to data points
• Descriptive analyses, which identify patterns in time series data such as cycles or trends
• Explanatory analyses, which explore and understand the relationships of data within collected data sets (such as cause and effect)
• Forecasting analysis models, which are used to predict future data performance. Forecasting is always based on historical trends

5. Time series analysis models and techniques

There are many different models and techniques that can be used to perform time series analyses. Let’s explore three of the most common models now.

Box-Jenkins ARIMA models

Box-Jenkins ARIMA models are univariate analysis models leveraged to understand one time-dependent variable, such as student performance over time, temperature over time, et cetera. ARIMA models are further used to predict future data points of those single, time-dependent variables.

To use the ARIMA model properly, data analysts must both account for and then remove seasonalities or other differences in past data points as much as possible. ARIMA models include terms that allow analysts to account for things like seasonal differences, moving averages, and other terms within the model so they can compensate for these effects.

Box-Jenkins multivariate models

Box-Jenkins multivariate models are, as the name suggests, helpful for analyzing more than one time-dependent variable. In this way, data analysts can examine how multiple variables change over time and potentially determine how those variables influence each other’s development.

One great example is temperature and humidity in meteorology. Meteorologists may use multivariate models to determine how temperature impacts humidity in local climates or vice versa. They can see how both of these effects change over time with the seasons and how time impacts their effects on each other.

Holt-Winters method

The Holt-Winters method is a useful time series analysis technique that relies on exponential smoothing. In short, the Holt-Winters method helps data analysts predict outcomes or future events. This method includes seasonality and cyclic data effects, thereby improving the accuracy of data forecasts.

6. Final thoughts

Ultimately, time series analysis is an important part of data analytics, particularly when predicting future events or making wise business decisions. Data analysts need to know how to perform time series analysis to better serve their clients and to understand how data points can evolve more thoroughly than by simply observing beginning and end data points on a graph.

Want to learn more about time series analysis and data analytics in general? Why not start by signing up for this free, 5-day, data analytics short course ? Alternatively, to learn more about other data analytics topics, be sure to check out the following introductory articles:

• What is linear regression?
• The best SQL certifications for aspiring data analysts
• The most-asked machine learning interview questions

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Time series analysis is a powerful tool for analysing data collected throughout an extended period. Here is how you can use it to understand changes in consumer and market trends, and make data-driven decisions.

Time series analysis provides businesses with valuable insights into their data by breaking it down into specific time periods or “waves”. Here are four market and pricing research areas in which time series analysis can help businesses of all sizes and industries identify trends, such as seasonality , cyclic behaviour , and hidden patterns in consumer and market trends , for better decision-making.

Discovering consumption patterns and market trends over time

In today’s fast-paced business environment, understanding how consumer and market trends shift is crucial for businesses to identify and capitalise on growth and innovation opportunities .

By conducting market research regularly and analysing the data using time series analysis, businesses can identify patterns, trends, and anomalies in consumer behaviours and market dynamics that might not be immediately obvious. This information can help businesses adjust their strategies and positioning in response to changes in the market, such as launching new products to address an unmet need or targeting specific groups of customers at different times of the year.

Monitoring changes in customers’ acceptable price ranges

Continuously measuring customers’ acceptable price ranges provides businesses with valuable insights into setting competitive prices for products and services in the rapidly changing market.

By conducting Van Westendorp Price Sensitivity Meter over an extended period and analysing the data with time series analysis, businesses can uncover customers’ acceptable price ranges at different times. This information can inform pricing and sales strategies, such as the price levels during peak periods and the best time and frequency for sales promotions or discounts, ensuring prices remain competitive while still maximising revenue.

Deep diving into consumer preferences and attitudes toward products and services over time

By analysing consumer preferences and attitudes over time, businesses can gain insight into which products or features are favoured by their customers. This helps businesses adjust their offerings to meet their customers’ needs better.

Additionally, businesses can make proactive changes, such as adjusting marketing strategies and implementing new customer service initiatives to improve customer satisfaction and increase sales by understanding which factors are most important to their customers.

Evaluating the effectiveness of claims and ad messages over time

In today’s competitive business landscape, tracking how consumers perceive product claims and advertising messages over time is crucial for a business to maintain the reliability , uniqueness , and relevance of claims and ad messages.

By conducting claim tests with their target audiences monthly or quarterly, businesses can stay aware of changes in consumer perceptions and adjust their products and marketing strategies to remain appealing to their customers.

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Time Series Analysis: A Quick Introduction with Examples

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We all know Coca-Coca, the conglomerate giant. The company makes millions of dollars each year and can seemingly anticipate every issue or new market trend. However, have you ever thought about how they stay on top of the game? It’s because their data science teams use time series analysis .

In this article, we’ll explore what this technique entails through real-world examples, and discuss the types of time series modeling you’re likely to encounter.

What Is Time Series Analysis?

In a management context, we are typically interested in forecasting certain types of outcomes . Some examples are sales (at a total or a division level), customer satisfaction levels, the company’s ability to achieve target cost levels, or capability to deliver successful projects. In all these cases, we’ll use past data to come up with a prediction about the future. Time series analysis is part of predictive analysis, gathering data over consistent intervals of time (a.k.a. collecting time series data ). It’s an effective tool that allows us to quantify the impact of management decisions on future outcomes.

Let’s take Coca-Cola again and look at a time series analysis example through the lens of the company’s sales. Two quarters from now, their expected sales will be anywhere between 250,000 and 300,000 units. Historical sales indicate a strong relationship between unit sales and weather – otherwise known as correlation analysis . Based on that, it is likely that the numbers will be closer to 290,000 in the summer months. However, to achieve similar results in the winter quarter, the company will need some additional marketing investments.  

The technique the Coca-Cola team can use to perform this type of future forecasting is precisely time series analysis. When applied, the model will provide a range of potential outcomes. In our example, the variable we are interested to predict is future sales volume. Therefore, the outcomes will vary depending on numerous factors, which may affect sales development throughout the year.

Let’s suppose the weather is 5% warmer than average, and Coca-Cola spend 5% more on marketing by investing in TV ads and promotional events. Then, based on historical data, we can reasonably expect that sales will be on the higher end of the range we indicated - 290,000 units. By changing the weather condition assumptions and running hypothesis testing on different marketing spend, the model would yield a separate time series analysis forecast. Typically, in practice, we will provide a range of estimates. For Coca-Cola, they might look something like this:

• 290,000 units in the best-case scenario
• 250,000 units in the worst-case scenario
• 270,000 in a base-case scenario

What Are the Types of Time Series Modelling Methods?

There are 4 modeling methods that analysts often use to support time series analysis:

• Probabilistic
• Deterministic

We’ll now explore each type and give you examples of how to apply them in a business setting.

Naive Time Series Method

A naive forecast – or persistence forecast – is the simplest form of time series analysis where we take the value from the previous period as a reference:

\[x_t = x_{t+1}\]

It does not require large amounts of data – one data point for each previous period is sufficient. Additionally, naive time series modeling can take seasonality and trend into account.

If you recall the Coca-Cola example, seasonality suggests that there is a cyclical pattern in the data that only appears periodically. Instead of taking the sales volume for the previous month, you can take last year’s value for the same month you’re trying to predict now:

In essence, you would be using last December’s numbers, instead of this November’s values, to forecast the sales for this upcoming December.

Another option is to consider the trend. For example, based on our historical analysis, we can see that last year’s September sales dropped 10% versus those made in August. We can use this information to forecast September of this year by applying the 10% reduction of sales versus the August ones:

The naive forecasting method is easy to understand and to use. However, the past is not always a good indicator of the future. That is why more sophisticated analytical techniques are often required to come up with more accurate sales forecasts.

Probabilistic Time Series Method

Probabilistic modeling is also known as a Monte Carlo simulation. It’s named after the gambling hot spot in Monaco as it simulates real-life events with uncertain outcomes.

When faced with significant uncertainty, the Monte Carlo Simulation allows you to use a range of input values rather than just replacing the uncertain variable with a number. More precisely, these input values make use of the variable’s distribution function and help obtain a large number of possible realizations of the output variable.

To illustrate, here is an example of a Monte Carlo simulation for a revenue forecast:

There is a 90% chance that total revenue will be between X and Y, and a 61.2% chance that the service will be higher than the forecast.

The advantage of Monte Carlo simulation is that it fully explores the probability distribution function of a certain variable. In our example, that’s the development of sales. Fortunately, we are able to study the probability of the sales that will fall within a certain bandwidth. Knowing this will help us manage risk.

However, to be successful, we need reliable data. If we do a Monte Carlo simulation and obtain no certainty that sales will fall within a specific bandwidth, then the probabilistic modeling has no added value.

Deterministic Time Series Method

The third method we’ll be looking at is the deterministic model – a more complex form of time series analysis that includes user-defined confidence intervals . As an example, let’s examine a historical trend and a forecast with a certain level of confidence for the year to come:

Suppose we want to see the sales forecast within a 95% range of certainty. Then, based on the graph, we can say with 95% certainty that we expect sales to be in the region from 240,000 to 280,000 units.

In other words, we provide an interval based on a deterministic trend, instead of making a definitive claim that we will make 265,000 sales. Thus, we have a better chance of preparing for the future because we know what the best- and worst-case scenarios look like.

Hybrid Time Series Method

The last type of time series analysis we will discuss is called hybrid modeling. As the name suggests, it combines two other types of models - probabilistic and deterministic. The hybrid model considers the available data, then steps on it to simulate how uncertainties can affect the output. 

For example, suppose we increase our marketing budget whilst having similar weather as last year. Then, we can expect a sales volume between 240,000 and 280,000 units with 90% certainty:

This is a multi-step process, so we don’t get these numbers right away. Instead, we first go with the deterministic approach to find a model which describes the data well. In most cases, this is some variation of an ARIMA model : $x = \alpha + \beta_1 x_{t-1} + \beta_2 x_{t-1}$ , etc.

Then, we expand it to include a trend or a seasonal component based on some manual analysis. After we find the best fitting model, we conduct a Monte Carlo simulation to see how a random variable with the same statistical parameters would evolve over time. Of course, the simulation conducts this forecast thousands of times. At the end of it, we get a range of the most frequently predicted values to create our 90% confidence interval.

Overall, we can say that hybrid modeling is the most popular approach as it combines two types of methods to give us the highest percentage of certainty possible.

Time Series Analysis: What’s Next?

Time series analysis brings exponential value to business development. Analysts utilize it to help companies estimate their revenue, predict trends, and future-proof their products.

As this type of analysis is part of business analytics, having it in your tool box means that you will be at a vital position in a company which offers heaps of career growth opportunities.

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Time series analysis is a statistical technique used to analyze and interpret sequential data points collected over time. This method of data analysis provides insights into the underlying patterns, trends, and behaviors of a given dataset with a different perspective than other statistical analyses. By making observations at equally spaced intervals, data professionals can make informed decisions based on historical trends, accurate predictions for better future outcomes, and impactful improvements in the areas that matter most to the organization.

Table of Contents

The Importance of Time Series Analysis

Time series analysis plays a pivotal role in extracting meaningful information from temporal data, enabling organizations to make informed decisions through uncovering patterns and trends that may not be immediately apparent in raw data. By identifying these temporal dependencies, organizations can gain insights into the factors influencing their operations, allowing them to continuously adapt to shifting business landscapes.

Learn more about the different types of data analysis .

How Does Time Series Analysis Work?

Time series analysis involves studying the temporal ordering of data points to uncover patterns, trends, and dependencies. It is typically composed of the following steps:

• Data collection— Gather relevant data over a specified time period. These activities could include daily stock prices, monthly sales figures, hourly temperature readings, or any other dataset with a temporal component.
• Data exploration— Examine the dataset for trends, seasonality, and outliers. Visualization tools such as line charts, bar graphs, and histograms are commonly used to gain a preliminary understanding of the data.
• Stationarity assessment— Check if the data is stationary, meaning its statistical properties remain constant over time. Stationarity is a crucial assumption for many time series models.
• Decomposition— Break down the time series into its components, typically trend, seasonality, and residuals. This decomposition activity helps in understanding the underlying patterns within the data.
• Modeling— Choose an appropriate time series model based on the characteristics of the data. Common models include autoregressive integrated moving average (ARIMA), seasonal-trend decomposition using locally estimated scatterplot smoothing (LOESS STL), and exponential smoothing state space models (ETS).
• Model evaluation— Assess the accuracy of the chosen model using statistical metrics such as mean absolute error (MAE) or root mean square error (RMSE). Evaluation activities ensure that your model effectively captures the patterns in the data.
• Prediction— Once a satisfactory model is selected, use it to make predictions about future data points (e.g., for forecasting and strategic decision-making).

Time Series Modeling

Modeling involves selecting the appropriate model based on the profile of your data. The three distinct time series analysis methods are ARIMA, STL, and ETS—each has its own strengths, drawbacks, and unique characteristics.

ARIMA is a widely used time series forecasting method that combines autoregressive (AR) and moving average (MA) components. It is effective in capturing both short-term dependencies through lagged observations (AR) and smoothing out irregularities (MA). ARIMA is suitable for stationary time series data and provides a flexible framework for modeling various patterns.

ARIMA is less adept at handling seasonality directly, and additional differencing might be required to achieve stationarity. Moreover, ARIMA assumes that the relationship between variables is linear, which can limit its effectiveness in capturing complex nonlinear trends.

STL is a non-parametric time series decomposition method that separates a time series into three components: seasonal, trend, and remainder. It is particularly effective in handling data with strong seasonality and irregularities. STL uses locally estimated scatterplot smoothing (LOESS) to decompose the time series into these components.

While STL excels at capturing seasonality and trends, it may be less suitable for data without clear patterns. Additionally, the decomposition may not work well if the data has irregularities or outliers, as LOESS can be sensitive to extreme values.

ETS models based on exponential smoothing are suitable for time series data with different levels of seasonality and trend. These models include error, trend, and seasonality components, allowing for flexibility in capturing various patterns. ETS models are adaptive, making them suitable for datasets with changing characteristics over time.

ETS models may struggle with handling long-term trends and can be sensitive to the choice of smoothing parameters. They are generally more suitable for shorter-term forecasting, and their performance may decline when applied to data with complex or nonlinear trends.

The proper application of ARIMA, STL, and ETS depends on the specific characteristics of the time series data and the goals of the analysis:

• ARIMA is versatile but assumes linearity
• STL is robust for seasonality, but may struggle with irregularities
• ETS models provide adaptability but might be less effective for long-term trends

Data professionals often experiment with multiple methods to determine the most suitable approach for their particular dataset and forecasting objectives.

Types of Time Series Analysis

Time series analysis encompasses various approaches, each tailored to address specific characteristics of the data. The following are some of the more common types.

Univariate Time Series Analysis

This involves analyzing a single variable over time, such as stock prices, temperature, or sales figures.

Multivariate Time Series Analysis

This approach examines the relationship between two or more variables over time. It’s particularly useful for analyzing the impact of multiple factors on a given outcome.

Frequency Domain Analysis

This approach focuses on the frequency components of a time series, revealing patterns that might be hidden in the time domain. Fourier analysis is a common technique in frequency domain analysis.

Time-Frequency Analysis

This type of analysis explores how the frequency components of a time series change over time. Wavelet analysis is a popular method of time-frequency analysis.

Longitudinal Data Analysis

This kind of analysis deals with repeated measurements taken from the same subjects over time, emphasizing individual growth or change.

Cointegration Analysis

Cointegration analysis examines the long-term equilibrium relationship between non-stationary time series, and is often used in financial and economic analyses.

Each of these types of time series analysis has its relative strengths and weaknesses—your methodology choice will depend on the nature of the data, your organization’s problem or target, and the goals of the analysis.

Benefits of Time Series Analysis

The application of time series analysis offers a multitude of benefits across various domains. Here are the most common:

• Pattern recognition— Time series analysis helps identify underlying patterns and trends within a dataset, providing valuable insights into the factors influencing the observed behavior.
• Forecasting— By analyzing historical data, time series models can make accurate predictions about future trends , facilitating proactive decision-making and strategic planning.
• Anomaly detection— Time series analysis is effective in detecting unusual events or outliers in a dataset. This is particularly crucial for industries where anomalies may indicate potential issues or threats.
• Optimization— Understanding temporal dependencies allows organizations to optimize processes and resource allocation, leading to increased efficiency and cost savings.
• Risk management— In finance and other industries, time series analysis is instrumental in assessing and managing risks associated with various factors, such as market fluctuations or supply chain disruptions.
• Resource planning— Businesses can use time series analysis to forecast demand for products or services, enabling efficient resource planning and inventory management.

The versatility of time series analysis makes it a valuable tool for decision-makers across different industries/sectors, enabling them to execute more informed, data-driven choices with better outcomes.

Cross Sectional Data vs. Time Series Data

While cross-sectional and time series data both involve the collection of data points, they differ in terms of their temporal characteristics. Cross-sectional data represents a snapshot of a population at a specific point in time—observations are collected from multiple subjects or entities simultaneously.

For example, a survey conducted at a particular moment to understand the preferences of consumers represents cross-sectional data. In contrast, time series data involves the collection of data points over successive time intervals (for example, daily, monthly, or yearly observations of a particular variable). Stock prices recorded every day for a year or monthly sales figures over several years are examples of time series data.

Different analytical methods apply to each type of data, so it’s important to understand these differences. While cross-sectional data analysis focuses on understanding differences between subjects at a specific point in time, time series analysis seeks to uncover patterns and trends within a variable over time.

Examples of Time Series Analysis

The following examples help to illustrate the practical application of time series analysis across different domains.

Financial Time Series Analysis and Stock Price Forecasting

Consider a scenario where an investor wants to predict the future prices of a particular stock. By analyzing historical stock prices using time series models such as ARIMA or GARCH, the investor can make informed decisions about buying or selling stocks based on forecasted trends.

Risk Management in Banking and Finance

Banks use time series analysis to assess the risk associated with lending, investment, and market activities. By analyzing historical data on loan defaults, interest rates, and economic indicators, banks can develop risk models to make more informed lending and investment decisions.

Business Time Series Analysis and Sales Forecasting

Retailers often employ time series analysis to forecast future sales based on historical data. By analyzing past sales patterns, seasonality, and other factors, businesses can optimize inventory management, marketing strategies, and resource allocation.

Financial Budgeting and Forecasting

Businesses rely on accurate financial forecasting to plan and allocate resources effectively. Time series analysis can be applied to historical financial data to predict future trends in revenue, expenses, and overall financial performance.

This helps organizations create more accurate budgets, set realistic financial goals, and make informed decisions about investments, expansions, or cost-cutting measures. Financial time series analysis is particularly valuable for CFOs and financial analysts looking for instruments to navigate dynamic economic environments and make strategic financial decisions.

Marketing Campaign Effectiveness

Businesses often run various marketing campaigns throughout the year to promote their products or services. Time series analysis can be employed to assess the effectiveness of these campaigns by tracking key performance indicators (KPIs) over time.

Metrics such as website traffic, conversion rates, and sales can be analyzed to identify patterns and trends associated with specific marketing initiatives. This analysis helps businesses optimize their marketing strategies by focusing on the most successful campaigns and adjusting those that may not be yielding the desired results.

Customer Satisfaction and Feedback Analysis

Understanding customer satisfaction is critical for businesses aiming to improve their products and services. Time series analysis can be applied to track customer feedback over time, whether it’s collected through surveys, reviews, or social media.

By analyzing the temporal patterns of customer sentiment, businesses can identify areas that consistently receive positive feedback or areas that may require attention. This information is invaluable for making continuous improvements to enhance overall customer satisfaction and loyalty.

Supply Chain Optimization

For manufacturing and retail organizations, optimizing the supply chain is crucial for efficiency and cost-effectiveness. Time series analysis can help businesses forecast demand for their products based on historical sales data.

By identifying seasonal trends, patterns, and potential disruptions, companies can optimize inventory levels, production schedules, and distribution processes. This ensures that products are available when needed, minimizes excess inventory costs, and improves overall supply chain management.

Employee Performance and Productivity

Human resources departments can utilize time series analysis to assess employee performance and productivity over time. By tracking key performance metrics, such as sales targets, project completion rates, or customer service response times, organizations can identify patterns and trends in employee performance. This analysis can contribute to more effective performance evaluations, identify training needs, and assist in resource allocation within the organization.

Bottom Line

Time series analysis is a powerful tool that enables organizations to extract valuable insights from temporal data—primarily by uncovering patterns and trends to guide decision-making. Understanding the temporal dependencies within data allows data professionals to forecast future trends, optimize resource allocation, and manage risks effectively.

Read What is Regression Analysis? to learn more about another essential data analysis method used for a wide range of business applications.

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Beginner's Guide to Time Series Analysis

Over the last few years we've looked at various tools to help us identify exploitable patterns in asset prices. In particular we have considered basic econometrics, statistical machine learning and Bayesian statistics.

While these are all great modern tools for data analysis, the vast majority of asset modeling in the industry still makes use of statistical time series analysis . In this article we are going to examine what time series analysis is, outline its scope and learn how we can apply the techniques to various frequencies of financial data.

What is Time Series Analysis?

Firstly, a time series is defined as some quantity that is measured sequentially in time over some interval.

In its broadest form, time series analysis is about inferring what has happened to a series of data points in the past and attempting to predict what will happen to it the future.

However, we are going to take a quantitative statistical approach to time series, by assuming that our time series are realisations of sequences of random variables . That is, we are going to assume that there is some underlying generating process for our time series based on one or more statistical distributions from which these variables are drawn.

Time series analysis attempts to understand the past and predict the future.

Such a sequence of random variables is known as a discrete-time stochastic process (DTSP). In quantitative trading we are concerned with attempting to fit statistical models to these DTSPs to infer underlying relationships between series or predict future values in order to generate trading signals.

Time series in general, including those outside of the financial world, often contain the following features:

• Trends - A trend is a consistent directional movement in a time series. These trends will either be deterministic or stochastic . The former allows us to provide an underlying rationale for the trend, while the latter is a random feature of a series that we will be unlikely to explain. Trends often appear in financial series, particularly commodities prices, and many Commodity Trading Advisor (CTA) funds use sophisticated trend identification models in their trading algorithms.
• Seasonal Variation - Many time series contain seasonal variation. This is particularly true in series representing business sales or climate levels. In quantitative finance we often see seasonal variation in commodities, particularly those related to growing seasons or annual temperature variation (such as natural gas).
• Serial Dependence - One of the most important characteristics of time series, particularly financial series, is that of serial correlation . This occurs when time series observations that are close together in time tend to be correlated. Volatility clustering is one aspect of serial correlation that is particularly important in quantitative trading.

How Can We Apply Time Series Analysis in Quantitative Finance?

Our goal as quantitative researchers is to identify trends, seasonal variations and correlation using statistical time series methods, and ultimately generate trading signals or filters based on inference or predictions.

Our approach will be to:

• Forecast and Predict Future Values - In order to trade successfully we will need to accurately forecast future asset prices, at least in a statistical sense.
• Simulate Series - Once we identify statistical properties of financial time series we can use them to generate simulations of future scenarios. This allows us to estimate the number of trades, the expected trading costs, the expected returns profile, the technical and financial investment required in infrastructure, and thus ultimately the risk profile and profitability of a particular strategy or portfolio.
• Infer Relationships - Identification of relationships between time series and other quantitative values allows us to enhance our trading signals through filtration mechanisms. For example, if we can infer how the spread in a foreign exchange pair varies with bid/ask volume, then we can filter any prospective trades that may occur in a period where we forecast a wide spread in order to reduce transaction costs.

In addition we can apply standard (classical/frequentist or Bayesian) statistical tests to our time series models in order to justify certain behaviours, such as regime change in equity markets.

Time Series Analysis Software

To date we have almost exclusively made use of C++ and Python for our trading strategy implementation. Both of these languages are "first class environments" for writing an entire trading stack. They both contain many libraries and allow an "end-to-end" construction of a trading system solely within that language.

Unfortunately, C++ and Python do not possess extensive statistical libraries. This is one of their shortcomings. For this reason we will be using the R statistical environment as a means of carrying out time series research. R is well-suited for the job due to the availability of time series libraries, statistical methods and straightforward plotting capabilities.

We will learn R in a problem-solving fashion, whereby new commands and syntax will be introduced as needed. Fortunately, there are plenty of extremely useful tutorials for R availabile on the internet and I will point them out as we go through the sequence of time series analysis articles.

QuantStart Time Series Analysis Roadmap

Previous articles to date on the topics of statistical learning, econometrics and Bayesian analysis, have mostly been introductory in nature and haven't considered applications of such techniques to modern, high-frequency pricing information.

In order to apply some of the above techniques to higher frequency data we need a mathematical framework in which to unify our research. Time series analysis provides such a unification and allows us to discuss separate models within a statistical setting.

Eventually we will utilise Bayesian tools and machine learning techniques in conjunction with the following methods in order to forecast price level and direction, act as filters and determine "regime change", that is, determine when our time series have changed their underlying statistical behaviour.

Our time series roadmap is as follows. Each of the topics below will form its own article or set of articles. Once we've examined these methods in depth, we will be in a position to create some sophisticated modern models for examining high-frequency data.

• Time Series Introduction - This article outlines the area of time series analysis, its scope and how it can be applied to financial data.
• Correlation - An absolutely fundamental aspect of modeling time series is the concept of serial correlation . We will define it and describe one of the biggest pitfalls of time series analysis, namely that "correlation does not imply causation" .
• Forecasting - In this section we will consider the concept of forecasting , that is making predictions of future direction or level for a particular time series, and how it is carried out in practice.
• Stochastic Models - We have spent some time considering stochastic models in the field of options pricing on the site, namely with Geometric Brownian Motion and Stochastic Volatility . We will be looking at other models, including white noise and autoregressive models.
• Regression - When we have deterministic (as opposed to stochastic ) trends in the data we can justify their extrapolation using regression models. We will consider both linear and non-linear regression, and account for serial correlation.
• Stationary Models - Stationary models assume that the statistical properties (namely the mean and variance) of the series are constant in time. We can use Moving Average (MA) models, as well as combine them with autoregressive models to form ARMA models.
• Non-Stationary Models - Many financial time series are non-stationary, that is they have varying mean and variance. In particular, asset prices often have periods of high-volatility. For these series we need to use non-stationary models such as ARIMA, ARCH and GARCH.
• Multivariate Modeling - We have considered multivariate models on QuantStart in the past, namely when we considered mean-reverting pairs of equities. In this section we will more rigourously define cointegration and look at further tests for it. We will also consider vector autoregressive (VAR) models [not to be confused with Value-at-Risk!].
• State-Space Models - State Space Modelling borrows a long history of modern control theory used in engineering in order to allow us to model time series with rapidly varying parameters (such as the $\beta$ slope variable between two cointegrated assets in a linear regression). In particular, we will consider the famous Kalman Filter and the Hidden Markov Model . This will be one of the major uses of Bayesian analysis in time series.

How Does This Relate to Other QuantStart Statistical Articles?

My goal with QuantStart has always been to try and outline the mathematical and statistical framework for quantitative analysis and quantitative trading, from the basics through to the more advanced modern techniques.

To date we have spent the majority of the time on introductory and intermediate techniques. However, we are now going to turn our attention towards recent advanced techniques used in quantitative firms.

This will not only help those who wish to gain a career in the industry, but it will also give the quantitative retail traders among you a much broader toolkit of methods, as well as a unifying approach to trading.

Having worked in the industry previously, I can state with certainty that a substantial fraction of quantitative fund professionals use very sophisticated techniques to "hunt for alpha".

However, many of these firms are so large that they are not interested in "capacity constrained" strategies, i.e. those that aren't scalable above 1-2million USD. As retailers, if we can apply a sophisticated trading framework to these areas, we can achieve profitability over the long term.

We will eventually combine our articles on time series analysis, with the Bayesian approach to hypothesis testing and model selection, along with optimised C++, R and Python code, to produce non-linear, non-stationary time series models that can trade at high-frequency.

Now that the QSForex software has approached viability for high-frequency backtesting of multiple currency pairs, we have a ready-made framework for testing these models out, at least on the foreign exchange markets.

The next article in the series will discuss correlation and why it is one of the most fundamental aspects of time series analysis.

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Time series analysis: a gentle introduction

Explore the fundamentals of time series analysis in this comprehensive article. Learn about key concepts, use cases, and types of time series analysis, and discover models, techniques, and methods to analyze time series data.

Introduction

The proliferation of technologies like IoT and mobile devices, the internet, data transmission methods, and cloud computing means we live in a data-centric world. And the ability to collect, analyze and derive meaningful insights from data is a crucial driver of success for organizations across nearly every sector.

There are many types of data that can be collected for analysis purposes. Among them, time series data. In a nutshell, time series data is a collection of observations or measurements recorded sequentially, typically at regular, consistent intervals (e.g., every second, every minute, hourly, daily, weekly, or monthly). Common examples of time series data include stock prices and measurements from telemetry devices (e.g., temperature or pressure sensors).

Time series data involves different types of variables that change over time. For example, altitude, latitude, longitude, and speed are four variables that define the location and velocity of a plane in the sky.

What is time series analysis?

Time series analysis refers to all the methods, techniques, and models you can use to monitor and extract insights from time series data and its evolution in time. For instance, if we were to analyze time series data collected from the plane we mentioned earlier, we would be able to answer questions like:

• What is the aircraft's current location and how long will it take to reach its destination?
• How well is the plane maintaining its speed and cruising altitude?
• Are there any sudden altitude drops or speed changes that could indicate potential safety concerns or turbulence?
• Are there any recurring patterns in flight data that suggest maintenance is required?
• Was the flight path the most efficient, or are there opportunities to save fuel and time in the future?

Why is time series analysis needed?

Companies and individuals rely on time series analysis to extract meaningful and actionable insights from data. Here’s a list of different ways time series analysis can be leveraged:  

• Forecasting . By analyzing time series data, organizations are empowered to predict the likelihood of future events and outcomes.
• Detecting trends and patterns . Analyzing time series data helps businesses identify patterns and trends, and understand their underlying causes.
• Understanding data relationships . Time series analysis enables organizations to understand the relationship between different data variables, and how they influence each other over time.
• Anomaly detection . Time series analysis is frequently used to identify unusual occurrences or anomalies.
• Risk management . Time series analysis can help in risk assessment and management by modeling and predicting adverse events or volatilities.
• Decision making . Many decision-making processes rely on understanding how a data variable changes over time. In such scenarios, time series analysis can inform and guide decisions.

Improving operational efficiency . Businesses can use time series analysis to gain real-time visibility into their operations. This way, they can allocate resources efficiently, minimize costs, and quickly react to changing conditions.

What is time series analysis used for?

Time series analysis has broad applications across different industries and disciplines. Depending on the use case, analysis can be performed on historical data, or in real time.

Analyzing historical data

Analyzing historical time series data is a good option in scenarios where you aim to identify long-term trends and patterns, and there’s no pressure or business need to extract insights instantly, as soon as data is collected. Instead, data can be analyzed at a later date. Examples include:

• Analyzing economic indicators to forecast economic growth or recession.
• Analyzing sales data from the past year to predict future sales trends.
• Analyzing past weather data to predict weather patterns and perform climate change studies.
• Analyzing energy usage from the last six months to identify patterns and improve efficiency.
• Analyzing website traffic data weekly to determine traffic patterns and predict conversion rates.
• Analyzing health data to predict the spread of diseases.

Real-time use cases

There are scenarios with a limited window of opportunity to extract insights from time series data and act on them. In such cases, data needs to be analyzed in real time, as soon as it becomes available. For instance:

Time series car data collected and visualized in real time using a waveform graph. Source .

Time series analysis: key concepts

We will now discuss some key concepts data enthusiasts need to be aware of if they plan to analyze time series data.

Time series vs. pooled vs. cross-sectional data

Time series data is one of the most frequent data structures used in statistical analysis. But how does it compare to other common types of data, specifically cross-sectional and pooled data? And how can you combine them to draw meaningful statistics and insights?

As previously mentioned, time series data consists of observations about how one or more variables evolve in time. For instance, a retail organization may collect sales figures at the end of every month to analyze the monthly sales of different product categories in its stores. The sales figures compiled over time form a time series data set.

On the other hand, cross-sectional data is like a snapshot that gives a glimpse of a particular situation or state at a specific point in time. For example, the retail business could collect cross-sectional data on the number and size of stores in various cities to analyze the distribution and growth of its presence across different regions.

Finally, pooled data is a combination of information from different sources into a single dataset. Pooled data often comprises time series information, as well as cross-sectional data. The retail organization might pool time series data on monthly sales revenue for multiple retail stores and cross-sectional data on store attributes (size, location, number of employees) to analyze sales trends and explore relationships between store characteristics and sales performance.

Time series components

There are several components that data scientists and analysts need to take into account when analyzing time series data:

• Trend refers to the overall evolution of data over a long period of time. Trends can be upward (increasing), downward (decreasing), or null (no clear or significant movement in the data series over time). Trend analysis is crucial for detecting long-term patterns and identifying potential opportunities or risks.
• Seasonality refers to periodic data variations that occur at regular time intervals. For example, suppose you're analyzing shopping habits over a calendar year. There’s a good chance you’ll see sales spike during holidays like Christmas and drop to lower levels for the rest of the year. Analyzing seasonality is essential to understanding repeatable patterns and improving forecasting accuracy.  
• Cyclicity implies data fluctuations that occur over a very long time period (years or even decades). Consider, for instance, a dataset of annual population growth for a country over several decades. Upon analyzing the data, you may observe a cyclic pattern where the population growth rate experiences periods of acceleration (e.g., during periods of economic prosperity), followed by periods of deceleration (e.g., during economic downturns). Cyclicity analysis enables us to uncover hidden patterns, identify recurring trends, improve forecasting, and enhance decision-making.  
• Randomness or irregularity implies unexpected, unpredictable, or uncommon events and scenarios that impact data somehow. Let's consider a daily stock price dataset. Stock prices are typically recorded at the end of each trading day. However, there may be instances where no trading activity occurred due to public holidays or market closures. As a result, there will be gaps or irregularities in the time series data, with missing data points on certain days. Failing to handle these irregularities (e.g., through techniques like data imputation and mean substitution) can lead to biased analysis results or inaccurate interpretations.

Learn more about:

• Seasonality
• Randomness/irregularity

Stationarity

In time series analysis, data can be classified as stationary and non-stationary. Here's how they are different:

• Stationary . Data remains relatively constant, with consistent statistical properties and relationships between data points.
• Non-stationary . Data and statistical properties change over time, indicating trends, seasonality, or patterns.

Stationary vs. non-stationary time series data. Source .

Most raw time series data, like stock prices, temperature, or electricity usage, is non-stationary because its stats change over time. Yet, many statistical models and prediction techniques work better with stationary data. That's because it's easier to model and predict something that stays consistent over time.

So, before analyzing time series data, you need to check if your data is stationary. You can do this using tests like Augmented Dickey-Fuller (ADF), Kwiatkowski-Phillips-Schmidt-Shin (KPSS), and Phillips-Perron (PP).

If your data turns out to be non-stationary, you can transform it to be stationary. This can be done in several ways, such as differencing, applying a logarithmic transformation, removing trends, or adjusting for seasonal changes.

Learn more about stationarity in time series analysis  

Autocorrelation

Autocorrelation is about understanding how a current data point is influenced by all past data points. It's basically comparing the same information at different points in time. For instance, when studying daily temperatures, autocorrelation tells us how today's temperature relates to those of previous days. If there's a high autocorrelation, today's temperature will likely be similar to yesterday's, while a low auto correlation suggests otherwise.

Meanwhile, partial autocorrelation focuses on the relationship between a current data point and a specific past data point, ignoring any other data points in between. It's like asking, "How much is today's weather influenced by the weather exactly two days ago, ignoring the influence of yesterday's weather?"

Autocorrelation and partial autocorrelation. Source .

Looking at autocorrelation and partial autocorrelation helps us spot patterns and trends over time in our data. This is useful when we're trying to make predictions about the future, like forecasting the weather or predicting stock market trends.

Learn how to calculate and plot autocorrelation and partial autocorrelation with Python

Types of time series analysis

There are numerous types of time series analysis. We cover the most common ones below; as you will see, each type of analysis has different characteristics and serves different purposes.

Classification involves assigning categories or labels to time series data. For example, in health monitoring, you could classify heart rate data into categories like “normal”, “arrhythmia”, or “tachycardia”. Techniques used for classification range from traditional machine learning to modern neural networks. 

Learn more about time series classification

Curve fitting refers to plotting time series data on a curve to investigate relationships between data variables. For example, curve fitting can be used to analyze a company's past sales data to predict future sales trends. Curve fitting often involves methods like moving averages and smoothing (we'll discuss these later in this article).  

Learn about curve fitting with Python

Segmentation is the process of splitting a time series dataset into separate segments. The goal is to break down the data into smaller and simpler chunks that are easier to manage and interpret. For instance, if you're analyzing hourly temperature data for a whole year, you might divide the data into daily segments, and analyze each day separately.

Learn about algorithmic methods for time series segmentation

The purpose of descriptive analysis is to understand patterns within time-based data. Descriptive analysis may include identifying the central tendency and dispersion, exploring seasonality, trends, and cycles, and detecting anomalies or outliers. For example, a descriptive analysis of sales data might reveal increased sales during the holiday season, indicating seasonality, or a gradual increase in sales over the years, suggesting a trend.

Learn more about time series descriptive analysis

Exploratory analysis involves visualizing the data, checking summary statistics, and examining stationarity and autocorrelation. The purpose is to identify patterns, trends, and anomalies. Let’s assume you want to analyze website traffic. In this scenario, exploratory analysis could reveal weekly cycles (higher visits on weekdays vs. weekends or vice versa), long-term trends (steady growth in traffic), and autocorrelation (one day's visits influencing the next).

Learn more about time series exploratory analysis

While exploratory analysis helps discover trends and patterns, explanatory analysis is about understanding why these patterns, trends, and anomalies occur. Explanatory analysis uncovers causal relationships between time series variables over time. For example, explanatory analysis can reveal how factors like weather and economic activity influence electricity demand. Note that explanatory analysis often requires the use of statistical models to examine dependencies, correlations, and causal effects between data variables. 

Learn more about explanatory analysis

Forecasting involves predicting future values of a time series based on past data and trends. Various techniques, such as ARIMA, exponential smoothing, and machine learning algorithms, can be used for forecasting. Forecasting is widely used in business and economics for demand, sales, and financial predictions, among others.

Learn more about time series forecasting

Intervention analysis helps assess the impact of an event on a time series dataset. For instance, if a company launches a new advertising campaign, intervention analysis can be leveraged to estimate the effect of the campaign on new revenue, by comparing sales before and after the launch of the campaign. Advanced models like ARIMA are frequently used when performing intervention analysis. 

Learn more about time series intervention analysis

Time series analysis models, techniques, and methods

There’s an abundance of statistical, mathematical, and machine learning techniques, methods, and models data professionals can use to analyze and extract value from time series data. Here’s a list of the most popular, commonly-used ones:

Autoregression

Autoregression is a way of predicting future data values based on past ones, by using regression equations. Think of it like forecasting tomorrow's weather using temperatures from previous days. This technique, which assumes a direct relationship between past and future values, is often applied in finance to estimate future stock prices.

Learn how to implement an autoregressive model for time series with Python

Moving average

The moving average technique smooths out short-term data fluctuations and highlights trends or cycles. Moving averages can be used on different windows of time. For example, if you’re analyzing website traffic, you could apply a moving average to a seven-day time period to identify trends. On the other hand, a utility company analyzing power usage might use a 24-hour moving average to smooth out hourly fluctuations and better understand the pattern of electricity consumption.

There are several different types of moving averages, including:

• Simple moving average (SMA) . Treats every data point equally. Suitable for analyzing longer time frames or scenarios where data doesn’t change rapidly (e.g., tracking average annual rainfall in a city).
• Weighted moving average (WMA) . Gives more importance to the most recent data points. Helpful when dealing with medium-term time frames or when data shows moderate fluctuations (for example, analyzing the most recent customer feedback).
• Exponential moving average (EMA) . Also a weighted average, but it assigns significantly more weight to the latest data points. It’s the best choice if you're dealing with data that shifts rapidly and you need to respond quickly to these changes (for instance, you’re monitoring real-time fluctuations in cryptocurrency values).

An example of using the moving average technique on stock market data. Source .

Learn how to calculate moving averages

ARMA, short for Autoregressive Moving Average, is a forecasting model that blends two mechanisms: autoregression and moving averages.

The autoregressive part indicates that the analysis output relies on prior data values. Think of this as today's weather depending on the past few days' weather. The moving average component, on the other hand, accounts for shifts in the data that the autoregressive part can't explain by itself. For example, a sudden heavy rainfall could drastically drop the temperature in a short period, which is something that would not be directly connected to the temperatures of the previous days.

ARMA is most useful when dealing with stationary time series data that shows no obvious trends or seasonal patterns. A practical use could be for a company making machine parts. They could use ARMA to predict how much raw material they'll need each week, assuming their needs don't have clear patterns or seasonal changes.

Learn more about the ARMA model

ARIMA and SARIMA

ARIMA, which stands for Autoregressive Integrated Moving Average, and SARIMA, or Seasonal Autoregressive Integrated Moving Average, are commonly used forecasting models. They're frequently implemented using the Box-Jenkins approach.

ARIMA is like an upgraded version of ARMA, and it's used for studying datasets that show trends. ARIMA combines elements of ARMA and differencing techniques to eliminate trends from time series, thus making data easier to analyze.

SARIMA takes things one step further. This model is used to analyze time series data showing a repeating pattern at certain times, like higher ice cream sales during summer — this is what we call seasonal variation.

One important thing to remember is that both ARIMA and SARIMA focus solely on one data variable, like temperature readings over time. They predict future values based on past trends in that data, without considering the influence of other factors.

Learn more about time series forecasting with ARIMA and SARIMA

Box-Jenkins multivariate models

The Box-Jenkins approach is often linked with single-variable forecasting models like ARIMA and SARIMA. But it can also be used with multi-variable (multivariate) models like VAR and VARMA. These latter models are great when you need to look at several variables that impact each other. For example, when you want to predict things like a country's GDP, inflation, and job rates - all of which affect one another - these models come in handy.

Learn more about multivariate time series analysis

Exponential smoothing

Exponential smoothing is a popular method in time series analysis. Like the exponential moving average, it calculates the average from past data points, with less importance given to older data. But while the exponential moving average is used to identify trends, the purpose of exponential smoothing is to predict future outcomes.

There are different types of exponential smoothing:

• Simple exponential smoothing - used for analyzing data without any noticeable trends or seasonal changes. For example, an internet service provider could use this method to forecast daily network usage in a data center.
• Double exponential smoothing (also known as Holt's linear exponential smoothing) - used for analyzing data with a clear trend over time. An example use case could be predicting the increasing number of app downloads for a popular mobile game.
• Triple exponential smoothing (or Holt-Winters exponential smoothing) - useful when data has both a trend and a seasonal pattern. For example, you can use this method to forecast hotel bookings in a tourist location, which typically rise during certain seasons (like summer) and increase yearly as the hotel becomes more well-known.

Learn more about exponential smoothing and time series analysis

Machine learning

Machine learning (ML) models and methods are becoming increasingly important for time series analysis, especially when dealing with large datasets. Technologies like RNN (recurrent neural network) and LSTM (long short-term memory networks) can capture complex patterns and dependencies in time series data. Plus, they can learn from historical values and make accurate predictions.

A key aspect of machine learning models in time series analysis is their applicability in real-time scenarios. ML models can integrate with streaming data sources, analyze large volumes of data, and generate real-time predictions or classifications. This is crucial for applications that require immediate responses, such as anomaly detection or real-time monitoring systems.

Learn about ML approaches for time series analysis

Python libraries for time series analysis

Due to its simplicity, readability, flexibility, and scalability, Python is the language of choice for many data professionals. A rich and diverse ecosystem of Python libraries is available to data scientists looking to analyze time series data. We list the most popular ones in the following table (note that they are all open source and free to use):

Challenges of time series analysis

While time series data has plenty of applications and brings plenty of benefits, analyzing it is a complex affair. What type(s) of analysis should you perform? What’s the best analysis model for your use case? How do you handle irregularities? How can you make data non-stationary? How do you account for seasonality? These are a few of the many questions and challenges you’ll have to address along the way.

But analyzing time series data is just the last step of a much bigger process. Before there’s anything to analyze, you first need to collect raw data, transform and process it, and store it somewhere. The emergence of data streaming and stream processing technologies in the past decade has revolutionized the field of time series analysis and data mining. These types of technologies allow us to collect, process, and analyze time series data as soon as it’s generated. This way, data can be used not only for historical analysis, but also to power real-time use cases like fraud detection and predictive maintenance in manufacturing.

However, building and managing a data pipeline that’s able to ingest, process, store, and analyze time series data in real time means more moving pieces, additional complexity, and extra headaches. See, for example, how hard it is to scale stream processing infrastructure to deal with vast volumes of data. Or learn about the challenges of handling streaming time series data .

The final point relates to machine learning. ML models are becoming increasingly used in time series analysis (especially for real-time use cases) — they’re significantly more efficient than manual analysis, and they’re well suited for handling vast amounts of high-frequency time series data. The tradeoff? There are numerous challenges involved in getting an ML model from prototype to production. Among them:

• It’s difficult and time-consuming to transform time series data into a suitable format for analysis.
• There are plenty of tough choices to make. For example, should you choose an ML algorithm that’s easier to scale, or one that’s harder to scale, but more accurate?
• Testing and deploying ML models can be a nightmare, especially for data scientists unfamiliar with ​​software development best practices and engineering monitoring tools.

There are significant knowledge and skill differences between data engineers and data scientists, the two main roles involved in ML time series analysis. This gap adds additional complexity and needs to be bridged somehow .

As we have seen, analyzing time series data is vital for numerous industries: finance and banking, meteorology, healthcare, manufacturing, software development, transportation, and many, many more. Time series data analytics enable organizations across the board to monitor and optimize their operations, discover trends and patterns, predict future outcomes, make data-driven decisions, and instantly react to changing conditions.

On the flip side, collecting, processing, and analyzing time series data to gain actionable insights can be a daunting undertaking. If you’re looking for a way to simplify the process of extracting value from time series data, consider giving Quix a try. Founded by Formula 1 engineers with intimate knowledge of high-velocity time series data, Quix is a Python stream processing platform.

With Quix, data scientists are empowered to collect time series data from various sources and process it in real time. Then they can build ML models to analyze data, test them with Git & CI/CD, and seamlessly deploy them to production​​ — all of this with minimum involvement from ML and data engineers.

To learn more about Quix and how we can help you build ML pipelines for time series data in days rather than months, check out our documentation and get started with a free account .

What’s a Rich Text element?

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A rich text element can be used with static or dynamic content. For static content, just drop it into any page and begin editing. For dynamic content, add a rich text field to any collection and then connect a rich text element to that field in the settings panel. Voila!

How to customize formatting for each rich text

Headings, paragraphs, blockquotes, figures, images, and figure captions can all be styled after a class is added to the rich text element using the "When inside of" nested selector system.

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Javier Blanco Cordero is Senior Data Scientist at Quix, where he helps customers to get the most out of their data science projects. He was previously a Senior Data Scientist at Orange, developing churn prediction, marketing mix modeling, propensity to purchase models and more. Javier is a masters lecturer and speaker, specializing in pragmatic data science and causality.

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Tutorial Playlist

Statistics tutorial, everything you need to know about the probability density function in statistics, the best guide to understand central limit theorem, an in-depth guide to measures of central tendency : mean, median and mode, the ultimate guide to understand conditional probability, a comprehensive look at percentile in statistics, the best guide to understand bayes theorem, everything you need to know about the normal distribution, an in-depth explanation of cumulative distribution function, a complete guide to chi-square test, a complete guide on hypothesis testing in statistics, understanding the fundamentals of arithmetic and geometric progression, the definitive guide to understand spearman’s rank correlation, a comprehensive guide to understand mean squared error, all you need to know about the empirical rule in statistics, the complete guide to skewness and kurtosis, a holistic look at bernoulli distribution, all you need to know about bias in statistics, a complete guide to get a grasp of time series analysis, the key differences between z-test vs. t-test, the complete guide to understand pearson's correlation, a complete guide on the types of statistical studies, everything you need to know about poisson distribution, your best guide to understand correlation vs. regression, the most comprehensive guide for beginners on what is correlation, a complete guide to get a grasp of time series analysis.

Lesson 18 of 24 By Aryan Gupta

Table of Contents

Time-series data is a collection of data points over a set period. Time-series analysis is a method of analyzing data to extract useful statistical information and characteristics. One of the study's main goals is to predict future value. When forecasting with time series analysis, which is extremely complex, extrapolation is required. However, the forecasted value and the associated uncertainty estimation can make the result extremely valuable.

Your Data Analytics Career is Around The Corner!

What Is Time Series Analysis?

Time-series analysis is a method of analyzing a collection of data points over a period of time. Instead of recording data points intermittently or randomly, time series analysts record data points at consistent intervals over a set period of time.

While time-series data is information gathered over time, various types of information describe how and when that information was gathered. For example:

• Time series data: It is a collection of observations on the values that a variable takes at various points in time.
• Cross-sectional data: Data from one or more variables that were collected simultaneously.
• Pooled data: It is a combination of cross-sectional and time-series data.

The variable varies according to the probability distribution , showing which value Y can take and with which probability those values are taken.

Yt = μt + εt 

Each instance of Yt  is the result of the signal μt

εt is the noise term here.

Why Do We Need Time-Series Analysis?

Time series analysis has a range of applications in statistics , sales, economics, and many more areas. The common point is the technique used to model the data over a given period of time.

The reasons for doing time series analysis are as follows:

• Features: Time series analysis can be used to track features like trend, seasonality, and variability.
• Forecasting: Time series analysis can aid in the prediction of stock prices. It is used if you would like to know if the price will rise or fall and how much it will rise or fall.
• Inferences: You can predict the value and draw inferences from data using Time series analysis.

Time Series Analysis Example

Non-stationary data—that is, data that is constantly fluctuating over time or is affected by time—is analyzed using time series analysis. Because currency and sales are always changing, industries like finance, retail, and e-commerce frequently use time series analysis. Stock market analysis, especially when combined with automated trading algorithms, is an excellent example of time series analysis in action.

Time series analysis can be used in - 

• Rainfall measurements
• Automated stock trading
• Industry forecast
• Temperature readings
• Sales forecasting

Consider an example of railway passenger data over a period of time. 

On the X-axis, we have years, and on the Y-axis, you have the number of passengers.

The following observations can be derived from the given data.

• Trend: Over time, an increasing or decreasing pattern has been observed. The total number of passengers has risen over time.
• Seasonality: Cyclic patterns are the ones that repeat after a certain interval of time. In the case of the railway passenger, you can see a cyclic pattern with a high and low point that is visible throughout the interval.

Time Series Analysis Types

Some of the models of time series analysis include - 

• Classification: It identifies and assigns categories to the data.
• Curve Fitting: It plots data on a curve to investigate the relationships between variables in the data.
• Descriptive Analysis: Patterns in time-series data, such as trends, cycles, and seasonal variation, are identified.
• Explanative analysis: It attempts to comprehend the data and the relationships between it and cause and effect.
• Segmentation: It splits the data into segments to reveal the source data's underlying properties. 

ARIMA is an acronym for Autoregressive Integrated Moving Average. The Box-Jenkins method is another name for this method.

Now you will explore the ARIMA parameters in detail:

• Autoregressive Component: AR stands for autoregressive, and is denoted by p. When the value of p is 0, it means there is no correlation in the series. When the value of p is 1, it means that the auto-correlation is up to one lag.
• Moving Average: Moving average is denoted by q. When q=1, it means that there is an error term.
• Integration: Integration is denoted by d. When the value of d is 0, the series is stationary. When the value of d is 1, the series is not stationary, and you can make it stationary by taking the difference. 

Time series analysis has a wide range of applications and is one of the most important areas of study. It plays an important role in forecasting models and meaningful statistical characteristics.

If you want to learn more about Data science and statistics, you should refer to our Data Analytics Certification Program . If you have any questions for us, please mention them in our comments section, and we will get back to you.

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About the author.

Aryan is a tech enthusiast who likes to stay updated about trending technologies of today. He is passionate about all things technology, a keen researcher, and writes to inspire. Aside from technology, he is an active football player and a keen enthusiast of the game.

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Time series analysis and forecasting are crucial for predicting future trends, behaviors, and behaviours based on historical data. It helps businesses make informed decisions, optimize resources, and mitigate risks by anticipating market demand, sales fluctuations, stock prices, and more. Additionally, it aids in planning, budgeting, and strategizing across various domains such as finance, economics, healthcare, climate science, and resource management, driving efficiency and competitiveness.

• What is a Time Series?

A time series is a sequence of data points collected, recorded, or measured at successive, evenly-spaced time intervals.

Each data point represents observations or measurements taken over time, such as stock prices, temperature readings, or sales figures. Time series data is commonly represented graphically with time on the horizontal axis and the variable of interest on the vertical axis, allowing analysts to identify trends, patterns, and changes over time.

Time series data is often represented graphically as a line plot, with time depicted on the horizontal x-axis and the variable’s values displayed on the vertical y-axis. This graphical representation facilitates the visualization of trends, patterns, and fluctuations in the variable over time, aiding in the analysis and interpretation of the data.

Table of Content

Components of Time Series Data

Time Series Visualization

Preprocessing time series data, time series analysis & decomposition, what is time series forecasting, evaluating time series forecasts, top python libraries for time series analysis & forecasting, frequently asked questions on time series analysis, importance of time series analysis.

• Predict Future Trends: Time series analysis enables the prediction of future trends, allowing businesses to anticipate market demand, stock prices, and other key variables, facilitating proactive decision-making.
• Detect Patterns and Anomalies: By examining sequential data points, time series analysis helps detect recurring patterns and anomalies, providing insights into underlying behaviors and potential outliers.
• Risk Mitigation: By spotting potential risks, businesses can develop strategies to mitigate them, enhancing overall risk management.
• Strategic Planning: Time series insights inform long-term strategic planning, guiding decision-making across finance, healthcare, and other sectors.
• Competitive Edge: Time series analysis enables businesses to optimize resource allocation effectively, whether it’s inventory, workforce, or financial assets. By staying ahead of market trends, responding to changes, and making data-driven decisions, businesses gain a competitive edge.

There are four main components of a time series :

• Trend : Trend represents the long-term movement or directionality of the data over time. It captures the overall tendency of the series to increase, decrease, or remain stable. Trends can be linear, indicating a consistent increase or decrease, or nonlinear, showing more complex patterns.
• Seasonality : Seasonality refers to periodic fluctuations or patterns that occur at regular intervals within the time series. These cycles often repeat annually, quarterly, monthly, or weekly and are typically influenced by factors such as seasons, holidays, or business cycles.
• Cyclic variations: Cyclical variations are longer-term fluctuations in the time series that do not have a fixed period like seasonality. These fluctuations represent economic or business cycles, which can extend over multiple years and are often associated with expansions and contractions in economic activity.
• Irregularity (or Noise): Irregularity, also known as noise or randomness, refers to the unpredictable or random fluctuations in the data that cannot be attributed to the trend, seasonality, or cyclical variations. These fluctuations may result from random events, measurement errors, or other unforeseen factors. Irregularity makes it challenging to identify and model the underlying patterns in the time series data.

Time series visualization is the graphical representation of data collected over successive time intervals. It encompasses various techniques such as line plots, seasonal subseries plots, autocorrelation plots, histograms, and interactive visualizations. These methods help analysts identify trends, patterns, and anomalies in time-dependent data for better understanding and decision-making.

Different Time series visualization graphs

• Line Plots: Line plots display data points over time, allowing easy observation of trends, cycles, and fluctuations.
• Seasonal Plots: These plots break down time series data into seasonal components, helping to visualize patterns within specific time periods.
• Histograms and Density Plots: Shows the distribution of data values over time, providing insights into data characteristics such as skewness and kurtosis.
• Autocorrelation and Partial Autocorrelation Plots: These plots visualize correlation between a time series and its lagged values, helping to identify seasonality and lagged relationships.
• Spectral Analysis: Spectral analysis techniques, such as periodograms and spectrograms, visualize frequency components within time series data, useful for identifying periodicity and cyclical patterns.
• Decomposition Plots: Decomposition plots break down a time series into its trend, seasonal, and residual components, aiding in understanding the underlying patterns.

These visualization techniques allow analysts to explore, interpret, and communicate insights from time series data effectively, supporting informed decision-making and forecasting.

Time Series Visualization Techniques: Python and R Implementations

Time series preprocessing refers to the steps taken to clean, transform, and prepare time series data for analysis or forecasting. It involves techniques aimed at improving data quality, removing noise, handling missing values, and making the data suitable for modeling. Preprocessing tasks may include removing outliers, handling missing values through imputation, scaling or normalizing the data, detrending, deseasonalizing, and applying transformations to stabilize variance. The goal is to ensure that the time series data is in a suitable format for subsequent analysis or modeling.

• Handling Missing Values : Dealing with missing values in the time series data to ensure continuity and reliability in analysis.
• Dealing with Outliers: Identifying and addressing observations that significantly deviate from the rest of the data, which can distort analysis results.
• Stationarity and Transformation: Ensuring that the statistical properties of the time series, such as mean and variance, remain constant over time. Techniques like differencing, detrending, and deseasonalizing are used to achieve stationarity.

Time Series Preprocessing Techniques: Python and R Implementations

Time Series Analysis and Decomposition is a systematic approach to studying sequential data collected over successive time intervals. It involves analyzing the data to understand its underlying patterns, trends, and seasonal variations, as well as decomposing the time series into its fundamental components. This decomposition typically includes identifying and isolating elements such as trend, seasonality, and residual (error) components within the data.

Different Time Series Analysis & Decomposition Techniques

• Autocorrelation Analysis: A statistical method to measure the correlation between a time series and a lagged version of itself at different time lags. It helps identify patterns and dependencies within the time series data.
• Partial Autocorrelation Functions (PACF) : PACF measures the correlation between a time series and its lagged values, controlling for intermediate lags, aiding in identifying direct relationships between variables.
• Trend Analysis: The process of identifying and analyzing the long-term movement or directionality of a time series. Trends can be linear, exponential, or nonlinear and are crucial for understanding underlying patterns and making forecasts.
• Seasonality Analysis: Seasonality refers to periodic fluctuations or patterns that occur in a time series at fixed intervals, such as daily, weekly, or yearly. Seasonality analysis involves identifying and quantifying these recurring patterns to understand their impact on the data.
• Decomposition: Decomposition separates a time series into its constituent components, typically trend, seasonality, and residual (error). This technique helps isolate and analyze each component individually, making it easier to understand and model the underlying patterns.
• Spectrum Analysis: Spectrum analysis involves examining the frequency domain representation of a time series to identify dominant frequencies or periodicities. It helps detect cyclic patterns and understand the underlying periodic behavior of the data.
• Seasonal and Trend decomposition using Loess : STL decomposes a time series into three components: seasonal, trend, and residual. This decomposition enables modeling and forecasting each component separately, simplifying the forecasting process.
• Rolling Correlation: Rolling correlation calculates the correlation coefficient between two time series over a rolling window of observations, capturing changes in the relationship between variables over time.
• Cross-correlation Analysis: Cross-correlation analysis measures the similarity between two time series by computing their correlation at different time lags. It is used to identify relationships and dependencies between different variables or time series.
• Box-Jenkins Method: Box-Jenkins Method is a systematic approach for analyzing and modeling time series data. It involves identifying the appropriate autoregressive integrated moving average (ARIMA) model parameters, estimating the model, diagnosing its adequacy through residual analysis, and selecting the best-fitting model.
• Granger Causality Analysis: Granger causality analysis determines whether one time series can predict future values of another time series. It helps infer causal relationships between variables in time series data, providing insights into the direction of influence.

Time Series Analysis & Decomposition Techniques: Python and R Implementations

Time Series Forecasting is a statistical technique used to predict future values of a time series based on past observations. In simpler terms, it’s like looking into the future of data points plotted over time. By analyzing patterns and trends in historical data, Time Series Forecasting helps make informed predictions about what may happen next, assisting in decision-making and planning for the future.

Different Time Series Forecasting Algorithms

• Autoregressive (AR) Model : Autoregressive (AR) model is a type of time series model that predicts future values based on linear combinations of past values of the same time series. In an AR(p) model, the current value of the time series is modeled as a linear function of its previous p values, plus a random error term. The order of the autoregressive model (p) determines how many past values are used in the prediction.
• Autoregressive Integrated Moving Average (ARIMA): ARIMA is a widely used statistical method for time series forecasting. It models the next value in a time series based on linear combination of its own past values and past forecast errors. The model parameters include the order of autoregression (p), differencing (d), and moving average (q).
• ARIMAX : ARIMA model extended to include exogenous variables that can improve forecast accuracy.
• Seasonal Autoregressive Integrated Moving Average (SARIMA) : SARIMA extends ARIMA by incorporating seasonality into the model. It includes additional seasonal parameters (P, D, Q) to capture periodic fluctuations in the data.
• SARIMAX : Extension of SARIMA that incorporates exogenous variables for seasonal time series forecasting.
• Vector Autoregression (VAR) Models: VAR models extend autoregression to multivariate time series data by modeling each variable as a linear combination of its past values and the past values of other variables. They are suitable for analyzing and forecasting interdependencies among multiple time series.
• Theta Method : A simple and intuitive forecasting technique based on extrapolation and trend fitting.
• Exponential Smoothing Methods: Exponential smoothing methods, such as Simple Exponential Smoothing (SES) and Holt-Winters, forecast future values by exponentially decreasing weights for past observations. These methods are particularly useful for data with trend and seasonality.
• Gaussian Processes Regression: Gaussian Processes Regression is a Bayesian non-parametric approach that models the distribution of functions over time. It provides uncertainty estimates along with point forecasts, making it useful for capturing uncertainty in time series forecasting.
• Generalized Additive Models (GAM): A flexible modeling approach that combines additive components, allowing for nonlinear relationships and interactions.
• Random Forests: Random Forests is a machine learning ensemble method that constructs multiple decision trees during training and outputs the average prediction of the individual trees. It can handle complex relationships and interactions in the data, making it effective for time series forecasting.
• Gradient Boosting Machines (GBM): GBM is another ensemble learning technique that builds multiple decision trees sequentially, where each tree corrects the errors of the previous one. It excels in capturing nonlinear relationships and is robust against overfitting.
• State Space Models: State space models represent a time series as a combination of unobserved (hidden) states and observed measurements. These models capture both the deterministic and stochastic components of the time series, making them suitable for forecasting and anomaly detection.
• Dynamic Linear Models (DLMs): DLMs are Bayesian state-space models that represent time series data as a combination of latent state variables and observations. They are flexible models capable of incorporating various trends, seasonality, and other dynamic patterns in the data.
• Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) Networks: RNNs and LSTMs are deep learning architectures designed to handle sequential data. They can capture complex temporal dependencies in time series data, making them powerful tools for forecasting tasks, especially when dealing with large-scale and high-dimensional data.
• Hidden Markov Model (HMM): A Hidden Markov Model (HMM) is a statistical model used to describe sequences of observable events generated by underlying hidden states. In time series, HMMs infer hidden states from observed data, capturing dependencies and transitions between states. They are valuable for tasks like speech recognition, gesture analysis, and anomaly detection, providing a framework to model complex sequential data and extract meaningful patterns from it.

Time Series Forecasting Algorithms: Python and R Implementations

Evaluating Time Series Forecasts involves assessing the accuracy and effectiveness of predictions made by time series forecasting models. This process aims to measure how well a model performs in predicting future values based on historical data. By evaluating forecasts, analysts can determine the reliability of the models, identify areas for improvement, and make informed decisions about their use in practical applications.

Performance Metrics:

Performance metrics are quantitative measures used to evaluate the accuracy and effectiveness of time series forecasts. These metrics provide insights into how well a forecasting model performs in predicting future values based on historical data. Common performance metrics which can be used for time series include:

• Mean Absolute Error (MAE) : Measures the average magnitude of errors between predicted and actual values.
• Mean Absolute Percentage Error (MAPE) : Calculates the average percentage difference between predicted and actual values.
• Mean Squared Error (MSE) : Computes the average squared differences between predicted and actual values.
• Root Mean Squared Error (RMSE) : The square root of MSE, providing a measure of the typical magnitude of errors.
• Forecast Bias: Determines whether forecasts systematically overestimate or underestimate actual values.
• Forecast Interval Coverage : Evaluates the percentage of actual values that fall within forecast intervals.
• Theil’s U Statistic: Compares the performance of the forecast model to a naïve benchmark model.

Cross-Validation Techniques

Cross-validation techniques are used to assess the generalization performance of time series forecasting models. These techniques involve splitting the available data into training and testing sets, fitting the model on the training data, and evaluating its performance on the unseen testing data. Common cross-validation techniques for time series data include:

• Train-Test Split for Time Series: Divides the dataset into a training set for model fitting and a separate testing set for evaluation.
• Rolling Window Validation: Uses a moving window approach to iteratively train and test the model on different subsets of the data.
• Time Series Cross-Validation : Splits the time series data into multiple folds, ensuring that each fold maintains the temporal order of observations.
• Walk-Forward Validation: Similar to rolling window validation but updates the training set with each new observation, allowing the model to adapt to changing data patterns.

Python Libraries for Time Series Analysis & Forecasting encompass a suite of powerful tools and frameworks designed to facilitate the analysis and forecasting of time series data. These libraries offer a diverse range of capabilities, including statistical modeling, machine learning algorithms, deep learning techniques, and probabilistic forecasting methods. With their user-friendly interfaces and extensive documentation, these libraries serve as invaluable resources for both beginners and experienced practitioners in the field of time series analysis and forecasting.

• Statsmodels: Statsmodels is a Python library for statistical modeling and hypothesis testing. It includes a wide range of statistical methods and models, including time series analysis tools like ARIMA, SARIMA, and VAR. Statsmodels is useful for performing classical statistical tests and building traditional time series models.
• Pmdarima: Pmdarima is a Python library that provides an interface to ARIMA models in a manner similar to that of scikit-learn. It automates the process of selecting optimal ARIMA parameters and fitting models to time series data.
• Prophet: Prophet is a forecasting tool developed by Facebook that is specifically designed for time series forecasting at scale. It provides a simple yet powerful interface for fitting and forecasting time series data, with built-in support for handling seasonality, holidays, and trend changes.
• tslearn: tslearn is a Python library for time series learning, which provides various algorithms and tools for time series classification, clustering, and regression. It offers implementations of state-of-the-art algorithms, such as dynamic time warping (DTW) and shapelets, for analyzing and mining time series data.
• ARCH: ARCH is a Python library for estimating and forecasting volatility models commonly used in financial econometrics. It provides tools for fitting autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) models to time series data.
• GluonTS: GluonTS is a Python library for probabilistic time series forecasting developed by Amazon. It provides a collection of state-of-the-art deep learning models and tools for building and training probabilistic forecasting models for time series data.
• PyFlux: PyFlux is a Python library for time series analysis and forecasting, which provides implementations of various time series models, including ARIMA, GARCH, and stochastic volatility models. It offers an intuitive interface for fitting and forecasting time series data with Bayesian inference methods.
• Sktime: Sktime is a Python library for machine learning with time series data, which provides a unified interface for building and evaluating machine learning models for time series forecasting, classification, and regression tasks. It integrates seamlessly with scikit-learn and offers tools for handling time series data efficiently.
• PyCaret: PyCaret is an open-source, low-code machine learning library in Python that automates the machine learning workflow. It supports time series forecasting tasks and provides tools for data preprocessing, feature engineering, model selection, and evaluation in a simple and streamlined manner.
• Darts: Darts (Data Augmentation for Regression Tasks with SVD) is a Python library for time series forecasting. It provides a flexible and modular framework for developing and evaluating forecasting models, including classical and deep learning-based approaches. Darts emphasizes simplicity, scalability, and reproducibility in time series analysis and forecasting tasks.
• Kats: Kats, short for “Kits to Analyze Time Series,” is an open-source Python library developed by Facebook. It provides a comprehensive toolkit for time series analysis, offering a wide range of functionalities to handle various aspects of time series data. Kats includes tools for time series forecasting, anomaly detection, feature engineering, and model evaluation. It aims to simplify the process of working with time series data by providing an intuitive interface and a collection of state-of-the-art algorithms.
• AutoTS : AutoTS, or Automated Time Series, is a Python library developed to simplify time series forecasting by automating the model selection and parameter tuning process. It employs machine learning algorithms and statistical techniques to automatically identify the most suitable forecasting models and parameters for a given dataset. This automation saves time and effort by eliminating the need for manual model selection and tuning.
• Scikit-learn: Scikit-learn is a popular machine learning library in Python that provides a wide range of algorithms and tools for data mining and analysis. While not specifically tailored for time series analysis, Scikit-learn offers some useful algorithms for forecasting tasks, such as regression, classification, and clustering.
• TensorFlow: TensorFlow is an open-source machine learning framework developed by Google. It is widely used for building and training deep learning models, including recurrent neural networks (RNNs) and long short-term memory networks (LSTMs), which are commonly used for time series forecasting tasks.
• Keras: Keras is a high-level neural networks API written in Python, which runs on top of TensorFlow. It provides a user-friendly interface for building and training neural networks, including recurrent and convolutional neural networks, for various machine learning tasks, including time series forecasting.
• PyTorch: PyTorch is another popular deep learning framework that is widely used for building neural network models. It offers dynamic computation graphs and a flexible architecture, making it suitable for prototyping and experimenting with complex models for time series forecasting.

Comparative Analysis of Python Libraries for Time Series

Python offers a diverse range of libraries and frameworks tailored for time series tasks, each with its own set of strengths and weaknesses. In this comparative analysis, we evaluate top Python libraries, which is commonly used for time series analysis and forecasting.

This table provides an overview of each library’s focus area, strengths, and weaknesses in the context of time series analysis and forecasting.

Python offers a rich ecosystem of libraries and frameworks tailored for time series analysis and forecasting, catering to diverse needs across various domains. From traditional statistical modeling with libraries like Statsmodels to cutting-edge deep learning approaches enabled by TensorFlow and PyTorch, practitioners have a wide array of tools at their disposal. However, each library comes with its own trade-offs in terms of usability, flexibility, and computational requirements. Choosing the right tool depends on the specific requirements of the task at hand, balancing factors like model complexity, interpretability, and computational efficiency. Overall, Python’s versatility and the breadth of available libraries empower analysts and data scientists to extract meaningful insights and make accurate predictions from time series data across different domains.

Q. What is time series data?

Time series data is a sequence of data points collected, recorded, or measured at successive, evenly spaced time intervals. It represents observations or measurements taken over time, such as stock prices, temperature readings, or sales figures.

Q. What are the four main components of a time series?

The four main components of a time series are: Trend Seasonality Cyclical variations Irregularity (or Noise)

Q. What is stationarity in time series?

Stationarity in time series refers to the property where the statistical properties of the data, such as mean and variance, remain constant over time. It indicates that the time series data does not exhibit trends or seasonality and is crucial for building accurate forecasting models.

Q. What is the real-time application of time series analysis and forecasting?

Time series analysis and forecasting have various real-time applications across different domains, including: Financial markets for predicting stock prices and market trends. Weather forecasting for predicting temperature, precipitation, and other meteorological variables. Energy demand forecasting for optimizing energy production and distribution. Healthcare for predicting patient admissions, disease outbreaks, and medical resource allocation. Retail for forecasting sales, demand, and inventory management.

Q. What do you mean by Dynamic Time Warping?

Dynamic Time Warping (DTW) is a technique used to measure the similarity between two sequences of data that may vary in time or speed. It aligns the sequences by stretching or compressing them in time to find the optimal matching between corresponding points. DTW is commonly used in time series analysis, speech recognition, and pattern recognition tasks where the sequences being compared have different lengths or rates of change.

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A Time Series Analysis-Based Stock Price Prediction Framework Using Artificial Intelligence

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• Harmanjeet Singh   ORCID: orcid.org/0000-0001-7109-1796 13 &
• Manisha Malhotra   ORCID: orcid.org/0000-0002-9056-9473 13  

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Forecasting stock prices have recently emerged as an essential component of the economic realm. Stock price forecasting is regarded as a challenging endeavor due to the volatility and noise of stock market activity. In many stock price prediction scenarios, the Facebook Prophet, LightGBM and ARIMAX models have been demonstrated to be competitive versus other models. This research presents an architecture based on a time series model, such as Facebook Prophet, Light Gradient Boost Machine (GBM), and Autoregressive Integrated Moving Average with Explanatory Variable (ARIMAX) to accurately predict stock prices. Experiments with multiple potential outcomes are conducted to evaluate the suggested framework using the stock price data set. The model was trained on ADANI stock price data over the previous fourteen years using Facebook Prophet, LightGBM and ARIMAX and evaluated using the Root Mean Square Error metric (RMSE).

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Singh, H., Malhotra, M. (2024). A Time Series Analysis-Based Stock Price Prediction Framework Using Artificial Intelligence. In: Challa, R.K., et al. Artificial Intelligence of Things. ICAIoT 2023. Communications in Computer and Information Science, vol 1930. Springer, Cham. https://doi.org/10.1007/978-3-031-48781-1_22

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