How can I receive as output from VGXVARX the p-value for each parameter in the Econometric Toolbox 2.0.1 (R2011b)?

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MathWorks Support Team 2011-9-29

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I tried the following example in doc on VGXVARX:

load Data_VARMA22
[EstSpec, EstStdErrors] = vgxvarx(vgxar(Spec), Y, [], Y0);
vgxdisp(EstSpec, EstStdErrors);

This will display "Parameter", "Value", "Std. Error", and "t-Statistic". I also want to know the "p-value" for each coefficient: the Pr > t.

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Answer 1

MathWorks Support Team 2011-9-29

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The t stat is the coefficient divided by the standard error. To compute a p-value, one needs the degrees of freedom of the error of the t distribution, dfe, which is the sample size minus the number of estimated parameters. To calculate a p-value, one can execute the following command:

pValue = 2*(tcdf(-|t|,dfe));

The t-statistic is used to test the hypothesis that the parameter being estimated is actually 0, thus it is irrelevant. Since the 95% confidence interval is about 2 standard errors on either side of the estimate, and the t statistic is just the estimate divided by the standard error, the rule of thumb is that a t stat with absolute value > 2 is significant, and rejects the hypothesis of a 0 parameter value. Hence one does not need the p-value.