hypothesis testing in eviews

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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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Stationarity in EViews

How to test for the existence of a unit root in eviews - stationarity of a series.

Greetings everyone! In this video, I will demonstrate how to test for the existence of a unit root in a time series using EViews software. Specifically, I will be using real data for Canada, consisting of the consumer price index. Our objective is to determine whether our series is stationary or non-stationary.

To achieve this, we will use three methods, starting with a visual inspection of the graph, followed by a correlogram analysis, and finally, formal tests including the Augmented-Dickey Fuller, KPSS, and Phillips-Perron tests.

Why do we care about stationarity in time series analysis?

Stationarity is a critical property of a time series that is frequently used in statistical modeling and analysis. When a time series is stationary, its statistical properties, such as the mean, variance, and autocorrelation, remain constant over time. This property allows for more accurate and reliable predictions and forecasts. In contrast, non-stationary time series can exhibit erratic and unpredictable behavior, making it difficult to model and forecast. By identifying and modeling the stationary components of a time series, analysts can better understand the underlying patterns and signals in the data, leading to more effective decision-making and forecasting.

We begin our stationarity analysis by taking a look at the graph. After analyzing the graph, we can observe that the series exhibits a trend and an intercept, indicating that the mean of the series changes over time, further suggesting non-stationarity. A visual graph of a non-stationary time series can display a changing pattern over time, including trends, seasonality, or cycles. The graph may indicate that the mean or variance of the data changes over time, making it challenging to identify any underlying pattern or signal in the data. Moreover, the graph may demonstrate high and persistent autocorrelations, which suggest a lack of independence between data points. In general, the visual graph of a non-stationary time series may show an inconsistent pattern over time, in contrast to a stationary time series graph that is relatively stable and consistent. 

 This observation is reinforced by the correlogram analysis which reveals a non-immediate decay in the auto-correlation function . A correlogram is a visual representation of the autocorrelation function (ACF) or partial autocorrelation function (PACF) of a time series. However, for non-stationary time series, where the statistical properties change over time, the correlogram may look distinct from that of a stationary series. In particular, non-stationary time series may exhibit slow or absent decay in autocorrelations, indicating trends or seasonality in the data. As a result, the correlogram of a non-stationary time series may display high and persistent autocorrelations, making it difficult to detect the true signal or pattern within the data. 

Next, we conduct the Augmented-Dickey Fuller test with a trend and intercept, as indicated by the graph. 

The augmented Dickey-Fuller (ADF) test is a statistical method used to determine whether a time series data set is stationary or non-stationary. The ADF test checks for the presence of a trend in the data by testing for the presence of a unit root. If a time series is stationary, its statistical properties such as the mean, variance, and autocorrelation remain constant over time. Conversely, when a time series is non-stationary, it has a trend or pattern that changes over time.

The ADF test is an extension of the Dickey-Fuller test that adds extra lagged terms in the regression equation to account for any serial correlation in the data. The ADF test produces a test statistic and a p-value. A series is considered stationary if the test statistic is less than the critical value and the p-value is less than a chosen significance level, typically 0.05. On the other hand, if the test statistic is greater than the critical value and the p-value is greater than the significance level, we fail to reject the null hypothesis, and conclude that the series is non-stationary.

The test results suggest that we cannot reject the null hypothesis of the series having a unit root, which confirms our suspicion of non-stationarity. 

We obtain similar outcomes from the Phillips-Perron test . 

The Phillips-Perron test is a popular statistical method for detecting stationarity in time series data, much like the Augmented Dickey-Fuller (ADF) test. However, the Phillips-Perron test utilizes a unique approach to account for autocorrelation and heteroscedasticity. By regressing the first difference of the series on a set of lagged differences, the test produces a test statistic and p-value. If the test statistic is less than the critical value and the p-value is less than the chosen significance level (usually 0.05), the null hypothesis that the time series is non-stationary can be rejected, and it can be concluded that the series is stationary. 

Furthermore, we use the KPSS test to determine if the series is stationary. The results of the KPSS test indicate that we can reject the null hypothesis of stationarity, again confirming the non-stationarity of our series.

The KPSS test is a statistical technique used to assess the stationarity of time series data by examining whether its trend is stationary around a mean or linear trend. Unlike the Augmented Dickey-Fuller (ADF) and Phillips-Perron tests, which detect the presence of a unit root indicating non-stationarity, the KPSS test checks the opposite .   Eviews produces a test statistic value, and if the statistical value is above the asymptotic critical values , we reject the null hypothesis of the test (null hypothesis: "the series is stationary"). The KPSS test is named after its inventors Kwiatkowski, Phillips, Schmidt, and Shin. 

In conclusion, the analysis of the graph, correlogram, and formal tests consistently suggest that the consumer price index time series for Canada exhibits non-stationarity, implying the existence of a unit root. We hope you found this video informative. If you have any questions or comments, please feel free to leave them in the comments section of the YouTube Video. Thank you for your attention.

Watch the video tutorial and download the dataset

Download Dataset

Learn how to conduct diverse unit root tests on multiple time series at the same time!

Recommended Literature

To comprehend the significance of stationarity in time series analysis, I recommend reading the renowned paper "Spurious Regressions in Econometrics" by Newbold and Granger (1974). This paper highlights the implications of employing non-stationary time series in regression analysis, specifically in economic and financial data analysis.

The authors explain how non-stationary time series can result in unreliable and misleading regression outcomes, known as "spurious" regression results. They also demonstrate that non-stationary series can appear highly correlated in a regression model, even when they are completely unrelated, leading to false conclusions and potentially harmful decisions.

Reading this paper can help you gain a comprehensive understanding of the concept of stationarity in time series analysis, its importance, and methods to detect and manage non-stationarity in your data. This classic paper is widely cited in the field of econometrics and time series analysis.

You can access the paper by clicking here .

I hope you find this recommendation valuable in your learning journey. Happy reading!

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hypothesis testing

Moderators: EViews Gareth , EViews Moderator

Post by emerito » Sun Dec 17, 2017 1:31 pm

Re: hypothesis testing

Post by startz » Sun Dec 17, 2017 3:42 pm

Post by emerito » Tue Dec 19, 2017 8:08 pm

Post by startz » Tue Dec 19, 2017 8:49 pm

Post by EViews Gareth » Tue Dec 19, 2017 9:54 pm

Post by emerito » Mon Dec 25, 2017 10:28 pm

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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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