hypothesis testing in eviews

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Post by Eoghan » Thu Apr 27, 2017 12:29 am

Re: hypothesis testing

Post by EViews Gareth » Thu Apr 27, 2017 12:44 am

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Interval Estimation and Hypothesis Testing by using EViews

1. interval estimation.

For the regression model y = β 1 +β 2 x + e, and under assumptions SR1-SR6, the important result that we use in this chapter is given in equation (3.3) of POE.

Using this result we can show that the interval b k ± t c se(b k ) has probability 1-a of containing the true but unknown parameter p*, where the “critical value” t c from a /-distribution such that P(t>t c ) = P(t < -t c ) = a/2

To construct interval estimates we will use EViews’ stored regression results. We will also make use of EViews built in statistical functions. For each distribution (see Function reference in EViews Help) four statistical functions are provided. The two we will make use of are the cumulative distribution (CDF) and the quantile (Inverse CDF) functions.

The for the /-distribution the CDF is given by the function @ctdist(x,v). This function returns the probability that a /-random variable with v degrees of freedom falls to the left of x. That is,

The quantile function @qtdist(p,v) computes the critical value of a /-random variable with v degrees of freedom such that probability p falls to the left of it. For example, if we specify tc=@qtdist(.975,38), then

To construct the interval estimates we require the least squares estimates bk and their standard errors se(bk). After each regression model is estimated the coefficients and standard errors are saved in the arrays @coefs and @stderrs. However they are saved only until the next regression is run, at which time they are replaced. If you have named the regression results, as we have (FOOD_EQ) then the coefficients are saved as well, with the names food_eq.@coefs and food_eq.@stderrs, respectively.

1.1. Constructing the interval estimate

Since we have estimated only one regression we can use the simple form for the saved results. Thus @coefs(2) = b2 and @stderrs(2) = se(b2). To generate the 95% confidence interval [b 2 – t c se{b 2 ), b 2 + t c se(b 2 )\ enter the following commands in the EViews command window, pressing the <Enter> key after each:

scalar tc = @qtdist(.975,38)

scalar b2 = @coefs(2)

scalar seb2 = @stderrs(2)

scalar b2_lb = b2 – tc*seb2

scalar b2_ub = b2 + tc*seb2

These scalar values show up in the workfile with the symbol #. For example, the value of the lower bound of the interval estimate is

1.2. Using a coefficient vector

While the above approach works perfectly fine, it may be nicer for report writing to store the interval estimates in an array and construct a table. On the main EViews Menu select Objects/New Object

We will create a Matrix-Vector-Coef named INT EST

It will be a coefficient vector that has 2 rows and 1 column

Click OK, and the empty array appears. Instead of all that pointing and clicking, you can simply enter on the command line

coef(2) int_est

Now, enter the commands

int_est(1) = @coefs(2) – @qtdist(.975,38)*@stderrs(2)

int_est(2) = @coefs(2) + @qtdist(.975,38)*@stderrs(2)

Here we have used the EViews saved results directly rather than create scalars for each elements. The vector we created is

Click on Freeze and then Name. We chose the name B2 INTERVAL ESTIMATE and it looks like this:

The advantage of this approach is that the contents can be highlighted, copied (Ctrl+C) and pasted (Ctrl+V) into a document. The resulting table can be edited as you like

2. RIGHT-TAIL TESTS

2.1. test of significance.

To test the null hypothesis that (3 2 = 0 against the alternative that it is positive (> 0), as described in Chapter 3.4.1a of POE, requires us to find the critical value, construct the /-statistic, and determine the /7-value.

• If we choose the a = .05 level of significance, then the critical value is the 95 th percentile of the /(3g) distribution.
• The /- statistic is the ratio of the estimate bi over its standard error, se(b 2 ).
• The /7-value is the area to the right of the calculated /-statistic (since it is a right-tail test). This value is one minus the cumulative probability to the left of the /-statistic.

The simplest set of commands is (do not type the comments in italic font)

scalar tc95 = @qtdist(.95,38)                           t-critical right tail

scalar tstat = b2/seb2                                       t-statistic

scalar pval = 1 – @ctdist(tstat,38)                    right-tail p-value

Alternatively, use the vector approach outlined in the previous section

Use the results of this vector to construct a table, such as

2.2. Test of an economic hypothesis

To test the null hypothesis that β 2 < 5 against tl alternative β 2 > 5 the same steps are executed, except for the construction of the t-statistic.

3. LEFT-TAIL TESTS

3.1. test of significance.

To test the null hypothesis that β 2 > 0 against the alternative that it is negative (< 0) requires us to find the critical value, construct the t-statistic, and determine the p-value.

• If we choose the a = .05 level of significance, then the critical value is the 5 th percentile of the t(38) distribution.
• The t- statistic is the ratio of the estimate b 2 over its standard error, se(b 2 ).
• The p-value is the area to the left of the calculated /-statistic (since it is a left-tail test). This value is given by the cumulative probability to the left of the t-statistic.

Alternatively

Note that we fail to reject the null hypothesis in this case, as expected.

3.2. Test of an economic hypothesis

To test the null hypothesis that β 2 >12 against the alternative that β 2 < 12, we use the same steps as above, except for the construction of the t-statistic.

The t-statistic value -.85 does not fall in the rejection region, and the p-value is about .20, thus we fail to reject this null hypothesis.

4. TWO-TAIL TESTS

4.1. test of significance.

The two tail test of the null hypothesis that β 2 = 0 against the alternative that β 2 # 0 we require the same test elements

• If we choose the a = .05 level of significance, then the right-tail critical value is the 97.5- percentile of the f ( 38) distribution and the left tail critical value is the 2.5-percentile.
• The t- statistic is the ratio of the estimate bi over its standard error, se(£>->).
• The p-value is the area to the left of minus the absolute value of the calculated t-statistic plus the area to the right of the absolute value of the calculated test statistic (since it is a two-tail test). This value is given by the cumulative probability to the left of the – |t-statistic| and l – the cumulative probability to the right of |t-statistic|.

The two tail p-value is

The test is carried out by EViews each time a regression model is estimated. If we examine FOOD_EQ, in the column labeled t-statistic is the ratio of the Coefficient to Std. Error. The column labeled Prob. contains the two-tail p-value for the test of significance. Note that the very small p-value is rounded to zero (to 4 places). For practical purposes this is enough since levels of significance below .001 are hardly ever used.

To use the coefficient vector approach

The result is as follows. Here we have copied the results from EViews at the highest precision to show that the p-value works out to be the same as reported above.

4.2. Test of an economic hypothesis

To test the null hypothesis that β 2 = 12.5 against the alternative β 2 # 12.5 the steps are the same as those above, except for the construction of the t-statistic.

Which yields

Source: Griffiths William E., Hill R. Carter, Lim Mark Andrew (2008), Using EViews for Principles of Econometrics , John Wiley & Sons; 3rd Edition.

20 Sep 2021

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Descriptive Statistics and Eviews

EViews has a lot to offer when it comes to data analysis, which includes descriptive statistics, impressive graphs, tests, and procedures as it understands the importance of statistical analysis s an important task to examine series and groups.

The fact that EViews is the most easy-to-use Statistical software, it understands all our needs to view different displays of our series, provides general statistics and statistics for time series, modify a series labels all with a just a set of clicks.

Taking an example, we have used GDP data of India from 1960 to 2019 measured in trillion dollars. The magical menus in Eviews for any series is the View and the Proc menu. The main data analysis can be done once you click on the View menu where all actions are divided into four blocks.

The first section views the data series in spreadsheet and Graph which is fully customizable in the Options tab.

The second section provides descriptive statistics and tests as well as one way tabulation of your series.

Descriptive statistics and tests-

This section of the View menu has various options allowing to get a deep statistical analysis of the data.

For Histogram & Stats Table –

Simply clicking on View/ Descriptive statistics and tests/ Histogram and stats

The results show the name of the series, the sample and the number of observations at top of the statistics panel.  EViews summarizes the main statistics for the series measuring central tendencies, Maximum and minimum values, standard deviation, skewness- the measure of asymmetry in data, kurtosis- The presence of fat tails, the Jarque-bera statistic and its associated p-value.

For Tabulation Analysis – View/ Descriptive statistics and tests/ One way Tabulation.

In this View EViews provides the counts, percentage counts and cumulative counts for each observation value.

Apart from descriptive statistics, EViews allows to carry out a number of formal hypothesis tests on a series namely

• Simple hypothesis tests – Tests for Mean, median and variance of the series.
• Equality Tests by Classification – Tests equality of means, medians and variance across subsamples of a series.
• Empirical Distribution Tests – Tests whether the data distribution of the series is drawn from a number of well-known distributions.

Simple hypothesis tests

One of the most common tests of series is to compare whether its mean is equal to a specific value. The GDP in our example can be tested for a mean of 600 trillion dollars if it is statistically significant.

• Open GDP series
• Click View/Descriptive statistics and tests/Simple Hypothesis Tests
• In the Series Distribution Tests dialog box, the test values can be added for Mean, Variance, and median.
• For Instance, we test the mean of ‘600 trillion dollars’ for the whole observations.

The results of the same appear and clearly the p-value is significant, and the null-hypothesis cannot be rejected.

Equality Tests by Classification

This view allows you to test equality of the means, medians and variances across sub samples of a single series.

For example, you can test whether mean income is the same for males and females, or whether the variance of education is related to race. The tests assume that the subsamples are independent.

Letting EViews know which series is to be classified

Empirical Distribution Tests

EViews provides built-in Kolmogorov-Smirnov, Lilliefors, Cramer-von Mises, Anderson-Darling, and Watson empirical distribution tests. These tests are based on the comparison between the empirical distribution and the specified theoretical distribution function.

You can test whether your series is normally distributed, or whether it comes from, among others, an exponential, extreme value, logistic, chi-square, Weibull, or gamma distribution. You may provide parameters for the distribution, or EViews will estimate the parameters for you.

To carry out the test, simply double click on the series and select  View/Descriptive Statistics & Tests/Empirical Distribution Tests…  from the series window.

The output of the test is shown in the screenshot and both the mean and variance is estimated. The value reports the asymptotic test statistics while the second column,  “Adj. Value”, reports test statistics that have a finite sample correction or adjusted for parameter uncertainty (in case the parameters are estimated). The third column reports p -value for the adjusted statistics.

All of the reported EViews  p -values will account for the fact that parameters in the distribution have been estimated.

The second part of the output table displays the parameter values used to compute the theoretical distribution function. Any parameters that are specified to estimate are estimated by maximum likelihood (for the normal distribution, the ML estimate of the standard deviation is subsequently degree of freedom corrected if the mean is not specified  a priori ). For parameters that do not have a closed form analytic solution, the likelihood function is maximized using analytic first and second derivatives. These estimated parameters are reported with a standard error and  p -value based on the asymptotic normal distribution.

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How to Interpret the Results of a Unit Root Test in Eviews

To interpret the results of a unit root test in EViews, you should consider the test statistic, p-value, and critical values. If the test statistic is less than the critical value, you may reject the null hypothesis of a unit root and conclude that the series is stationary.

The p-value indicates the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. If the p-value is less than the significance level, typically 0.05, you may reject the null hypothesis. EViews provides a variety of unit root testing tools, including the Augmented Dickey-Fuller (ADF) test, HEGY test, Canova and Hansen test, and Variance Ratio tests.

You can run a unit root test by specifying the series and the test type in EViews, such as the ADF test, Phillips-Perron test, or other relevant tests. It’s important to ensure that the series is stationary before performing further analysis, such as time series modeling or forecasting.

You can refer to EViews tutorials and resources available on platforms like YouTube and EViews forums for step-by-step guidance on conducting unit root tests and checking for stationarity in EViews

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Parameter Estimation and Hypothesis Testing in Linear Models

• © 1999
• Latest edition
• Karl-Rudolf Koch 0

Institute of Theoretical Geodesy of the University of Bonn, Bonn, Germany

You can also search for this author in PubMed   Google Scholar

• Based on a course on "Least Squares Adjustment and Statistics"
• The book is self-contained
• Includes supplementary material: sn.pub/extras

583 Citations

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Statistical Inference

• Probability distribution
• Probability theory
• analysis of variance
• confidence regions
• hypothesis testing
• linear models
• parameter estimation

Table of contents (5 chapters)

Front matter, introduction.

Karl-Rudolf Koch

Vector and Matrix Algebra

Probability theory, parameter estimation in linear models, hypothesis testing, interval estimation and test for outliers, back matter, authors and affiliations, bibliographic information.

Book Title : Parameter Estimation and Hypothesis Testing in Linear Models

Authors : Karl-Rudolf Koch

DOI : https://doi.org/10.1007/978-3-662-03976-2

Publisher : Springer Berlin, Heidelberg

eBook Packages : Springer Book Archive

Copyright Information : Springer-Verlag Berlin Heidelberg 1999

Hardcover ISBN : 978-3-540-65257-1 Published: 01 April 1999

Softcover ISBN : 978-3-642-08461-4 Published: 07 December 2010

eBook ISBN : 978-3-662-03976-2 Published: 09 March 2013

Edition Number : 2

Number of Pages : XX, 334

Additional Information : Original German edition published by Dümmlers, Bonn

Topics : Probability Theory and Stochastic Processes , Geophysics/Geodesy , Mathematical and Computational Engineering , Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences

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