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Aug 2, 2015 at 8:42 comment added Richard Hardy 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.
Aug 2, 2015 at 8:33 comment added Richard Hardy 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.
Aug 2, 2015 at 7:48 history edited Richard Hardy CC BY-SA 3.0
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S Jul 1, 2015 at 14:00 history suggested Learner CC BY-SA 3.0
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Jul 1, 2015 at 13:41 review Suggested edits
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Jul 1, 2015 at 13:30 history asked noclue11 CC BY-SA 3.0