# Do data and residuals of a VAR model have to be of normal distribution?

Does vector autoregression (VAR) model require data to be of normal distribution? What are the pitfalls if the residuals are not of normal distribution?

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The question is too general(vague). Please, try to focus on the aspects you are interested on. – user10525 Apr 13 '12 at 10:35
VAR models are regressions. Hence the usual regression assumptions apply. On the other hand, since VAR model admits MA($\infty$) representation, if errors are normal then the data should be normal too. The coefficients are usually estimated using OLS, hence their estimates are robust to non-normal disturbances. However if you have cointegration, the usual tests are sensitive to normality, if I remember correctly. – mpiktas Apr 13 '12 at 11:48

Thank you. From what I understood for linear regression Yi = b0 + b1*Xi + ei,

1) b1 ~ N( ) requires Yi ~ N( ).

a) Thus, I don't need Xi to be normal.

b) And Yi not being normal => b1 not normal


If I only want to get the coefficients but are not using the p-values, I don't need Yi to be normal.

2) a) E(ei) = 0 and "ei have constant variance and are uncorrelated"

=> b) E(b1) = beta1; and

c) "b1 has minimum variance among all unbiased linear estimators of beta1"


If I don't need (2b) and (2c), I don't need (2a).

Am I right?

P.S. Does anyone know how to get the p-values of the coefficients if I am using mAr.est() in R?

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 Please either update your question, or post a new one mentioning this one. Answers are for answering. Judging by your text, 2 separate questions can be asked. – mpiktas May 14 '12 at 7:44