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I'm trying to build a model to predict the volatility for a financial asset with ARIMA-GARCH model. (I use log returns as data)

I fit my ARIMA model with AIC and I did Engle’s Test to ensure there is a ARCH effect in the residuals of ARIMA model. However, the problem came after when I finished fitting my GARCH model, I implemented Engle’s Test again, and sadly, there was still ARCH effect left. So I keep tuning the parameters for my GARCH, yet it's not working.

Am I doing something wrong? If not, how can I fix the problem?

Big thank you in advance!!

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    $\begingroup$ How does your estimated model look like, how many lags do you include? Do you get the same behaviour if you choose lags based on HQIC or BIC? You choose the lags of the ARIMA and GARCH process based on these information criteria? Conduct likelihood ratio tests if you get conflicting results. Do you assume normally distributed shocks? Does your input data have ARCH effects? $\endgroup$ – Kevin Apr 28 '20 at 9:22
  • $\begingroup$ @KeSchn thanks for the directions! $\endgroup$ – eric Apr 28 '20 at 14:31
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    $\begingroup$ Engle's test is invalid for residuals of an (G)ARCH model, you should use Li-Mak test instead. This might not solve your problem, but will at least fix a part of it. Also, you should be testing standardized residuals of the (G)ARCH model, not raw residuals; depending on the software you are using, it can be easy to mix up the two. $\endgroup$ – Richard Hardy May 16 '20 at 10:12
  • $\begingroup$ @RichardHardy Thanks! $\endgroup$ – eric May 21 '20 at 14:36

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