I have a time series of logarithmic returns. After inspection of the ACF and PACF plots, I tried to fit AR(2), MA(2) and ARMA(1,1) models and eventually found out that the AR(2) version can possibly fit best.
The AR(2) model has no constant, no trend, no seasonality features and is stationary. So a very basic one.
However, when I checked for i.i.d.-ness of the residuals I discovered that, even though they're almost perfectly symmetric and serially uncorrelated, they still show some leptokurtosis.
My questions are:
- Can I tolerate the presence of such a leptokurtosis? Or should I proceed to modeling the squared errors with some ARCH-GARCH process?
- In the case I effectively should, can anyone provide me with a link for a guide on how to carry out combined ARIMA+GARCH analyses in R? I've already browsed for it for days but found nothing enlightening.