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I have some transformed data set (windspeeds that are nearly-weibull-distributed). I transformed this data which results in near-normal distribution (close to no excess kurtosis and skewness of zero).

Now, I want to remove the auto-correlation of the series and fit it (after detrending) to an auto-regressive model (tested various versions, ARMA, SARMA etc.). While increasing the number of lags for the AR and MA components reduces the autocorrelations to some extent, the residuals become more non-normal after 2 or 3 lags.

E.g. for an AR(1) model the residual's excess kurtosis is 4, for another additional lag it turns to 80.

I am a bit puzzled on how to best proceed from this point. On the one hand I want to remove the autocorrelations in a meaningful way, but trading this for non-normal residuals seems wrong as well. I read that if you have enough observations non-normal residuals could theoretically be ignored due to the asymptotic properties of the maximum likelihood estimator.
Any help greatly appreciated..

(EDIT: I would also like to proceed with the above with a multivariate analysis, so use some kind of VAR model.)

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  • $\begingroup$ I have never heard of a phenomenon that residual kurtosis is supposed to increase with the number of lags. That might be a coincidence. An answer by Rob J Hyndman here and a comment by Zachary Blumenfeld here (with a link to back up the claim) state that normality is not necessary asymptotically, so perhaps could could ignore it. $\endgroup$ – Richard Hardy Aug 2 '15 at 8:33
  • $\begingroup$ Or perhaps you could try different distributional assumptions if the software you are using allows for that. In R, package "rugarch" has a broad selection of distribution assumptions for ARFIMA models; since ARIMA is just a special case of ARFIMA, it should work. $\endgroup$ – Richard Hardy Aug 2 '15 at 8:42

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