Testing for Remaining ARCH Effects After ARIMA-GARCH Fitting

Summary

The document describes a volatility-modeling workflow using log returns. The author selects an ARIMA specification with the Akaike information criterion, then applies Engle’s test to the ARIMA residuals to check for conditional heteroskedasticity. After fitting a GARCH model, the author repeats the test and reports that ARCH effects remain, despite trying different parameter settings.

This is a useful diagnostic question because a fitted GARCH model should be assessed through its residual behavior, not assumed adequate merely because it converged. However, the document provides no answer or evidence that identifies the cause of the remaining effect, and it does not specify the model orders, test implementation, sample, or significance threshold. It therefore illustrates a problem in model checking rather than teaching a resolution. The result alone cannot establish that the implementation is wrong; model specification, distributional assumptions, residual choice, and test setup would need examination.

Key ideas

• The workflow fits an ARIMA model to log returns before modeling conditional volatility.
• Engle’s test is applied to ARIMA residuals to check for ARCH effects.
• The author reports remaining ARCH effects after fitting and testing a GARCH model.
• The document raises a diagnostic issue but gives no solution or details sufficient to identify its cause.

Tags

# The residuals of GARCH model reject Engle’s Test despite large parameters


# The residuals of GARCH model reject Engle’s Test despite large parameters












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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