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I fitted an ARIMA model on a time series and then did an ARCH-LM Test which shows heteroscedasticity. So I want to get an ARIMA-GARCH model.

My question: Do I need to reestimate the parameters of ARIMA (that I got initially without GARCH) together with the GARCH parameters, or do I keep the same ARIMA parameters and only estimate GARCH parameters?

Richard Hardy
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Jariel
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    This may be a duplicate question. The issue has been discussed in multiple posts. Start [here](http://stats.stackexchange.com/questions/87600/arma-garch-estimation-in-sequence) or [here](http://stats.stackexchange.com/questions/143517/arma-garch-estimation-process-in-practice) and check also related questions (panel on the right). A short answer: in general, you cannot first estimate ARIMA and then GARCH. In some special cases you may get away with inefficiency, but generally you will encounter inconsistency. – Richard Hardy Aug 11 '15 at 11:51

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