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I developed a Vector Autoregression (VAR) model of the first differenced for 35 observations including 3 variables, the maximum lag length based on AIC and SC was determined as p=1. My main objective is to determine Granger-causality. Running a check on my VAR model for residual test, it passed the test of no residual autocorrelations and serial correlation but the null hypothesis for the normality test and heteroskedasticity test was rejected.

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Should the results of the Granger-causality test be trusted?

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  • $\begingroup$ Two observations. A) I can't understand what the phrase "model of the first differenced for 35 observations including 3 variables" means, so it might be ambiguous to other people as well. B) What do you mean by "Is my model correct or wrong to test Granger-causality?"? Are you asking if the results of the Granger-causality should be trusted? Or something else? $\endgroup$ – oneloop Mar 28 '18 at 10:58
  • $\begingroup$ Should we understand that "35 observations" means "sample size 35"? Maybe I'm just being thick. I think I got it now. $\endgroup$ – oneloop Mar 28 '18 at 11:13
  • $\begingroup$ I meant a VAR model of the first differences of the variables, yes with a sample size of 35. Please my Question is; Should the results of the Granger causality be trusted in this case? $\endgroup$ – Lionel Mbanda Mar 28 '18 at 12:02
  • $\begingroup$ Does the results for granger causality test be trusted in this case for this VAR model? How can i be certain the results i have for granger causality are valid? $\endgroup$ – Lionel Mbanda Mar 28 '18 at 12:35
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Should the results of the Granger-causality test be trusted?

A Granger-causality test is a test of zero restrictions on some regression coefficients. Such tests, whether in Wald, Lagrange multiplier or likelihood ratio form, assume normality of the regression coefficients. The assumption may hold either because the model errors are normally distributed* or in large samples because of the central limit theorem. In this case you have neither; the residuals are nonnormal and the sample is quite small so we cannot rely on asymptotic normality. Hence, the test results are not reliable.

*as the coefficients are weighted and shifted linear combinations thereof by $\hat\beta=(X'X)^{-1}X'y=(X'X)^{-1}X'(X\beta+\varepsilon)=\beta+(X'X)^{-1}X'\varepsilon$, assuming the model is correct

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