Do I need to account for heteroskedasticity when performing the (vector) AR1-2 test?
The Autocorrelation (AR) 1-2 test is defined as follows - often referred to as the Breusch–Godfrey test (Wiki link):
The test is performed through the auxiliary regression of the residuals on the original variables and lagged residuals (missing lagged residuals at the start of the sample are replaced by zero, so no observations are lost). Unrestricted variables are included in the auxiliary regression. The null hypothesis is no autocorrelation, which would be rejected if the test statistic is too high. This LM test is valid for systems with lagged dependent variables and diagonal residual autocorrelation, whereas neither the Durbin--Watson nor the residual autocorrelations provide a valid test in that case.
I have a VAR model and I'm trying to determine the amount of lags to include. My model suffers from heteroskedasticity so I'm using the Wald test to take that into account when doing inference. There is a large difference between the normal standard errors and the heteroskedasticity-consistent standard errors in my model.
I'm using OxMetrics and it returns the same AR1-2 test statistic both when I estimate the model with normal errors and heteroskedasticity-consistent errors. Is this because the test on the auxiliary regression is not affected by the heteroskedasticity in the main model or is it just because OxMetrics doesn't perform the right test in this case?