Hi. I'm running a multivariate GARCH model. When I introduce un AR(1) in the mean equation, all the diagnostic tests on Standardized Residuals and squared residuals are perfect (Q-Statistics, Hosking's Multivariate Portmanteau test, Li and McLeod's Multivariate Portmanteau tests), however, the AR(1) parameter is not significant. When I remove the AR(1), Hosking's Multivariate Portmanteau Statistics are significant (autocorrelation problem is both residuals and squared residuals). It's a surprising result!!! especially that Hosking and McLeod's portmanteau tests give different results!
Do I have to keep the AR(1) even when it's not significant?
Thanks in advance for any advice.
I suggest you read the modified multivariate portmanteau test suggested by Hosking (1980). Hosking, J. R. M. (1980). "The Multivariate Portmanteau Statistic". Journal of American Statistical Association, 75, 602-608. However the portmanteau test statistic can be applied directly on the output objects from the built in R functions ar(), ar.ols(), ar.burg(), ar.yw(), ar.mle(), arima(), arim0(), Arima(), auto.arima(), lm(), glm(), and VAR(), it works with output objects from any fitted model. In this case, users should write their own function to fit any model they want, where they may use the built in R functions FitAR(), garch(), garchFit(), fracdiff(), tar(), etc. The object obj represents the output of this function. This output must be a list with at least two outcomes: the fitted residual and the order of the fitted model (list(res = ..., order = ...)). See the following example with the function FitModel().
Thank you Leonardo Mataruna for your help. I'm not really familiar with R, I'm using Rats, STATA, EVIEWS. I'll take a look at the reference you sent me.
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