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How to deal with conditional heteroskedasticity in ARIMA model?

ARCH test on ARIMA model indicates the presence of conditional heteroskedasticity and ARIMA forecasts are therefore incorrect.

Is there any way to fix it apart from using GARCH model ?

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  • $\begingroup$ Why do you want to avoid just adding a GARCH model on top of ARIMA? I.e. keep the conditional mean equation as in ARIMA but instead of having a constant conditional variance allow it to vary over time as in GARCH. $\endgroup$
    – Richard Hardy
    Jun 8, 2018 at 11:59

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Remedies often have side effects like suicide when an aspirin is all that is needed to eliminate a headache. Pulse outliers and/or seasonal pulses (untreated) can often incorrectly suggest " unwarranted complicated remedies" like power transforms , weighted least squares and arch/garch solutions. Keep the model as simple ( but not too simple !) in order to efficiently/correctly segment signal and noise. I am not arguing for an under-specified solution/remedy just one that is minimally sufficient. In my approach there are many solutions !

If you would like please post your data and I can be more specific as it relates to your data.

In response to the OP's comment

heteroskedasticity is a symptom ..the possible causes are multiple .. only your data knows for sure .. post your data and I will suggest a minimally sufficient "transformation" that results in a model error variance that is constant over time . That transformation could be as simple as adding a level shift , a seasonal pulse , a pulse or a local time trend.... OR incorporating weights to deal with an error variance that changes deterministically over time OR a change in parameters over time OR a dependence of the error variance and the level of the series over time OR an error variance that changes stochastically over time OR even an augmentation to your proposed arima model. Please post your model and parameters along with your data..

Many software packages often deal presumptively with complexity ... sometimes too complex ... where less intrusive solutions are superior due to their unstated software limitations ...

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    $\begingroup$ My model has the lowest AIC and seems to capture autocorrelation. I think signal and noise are already efficiently segmented. What would be the best way to deal with heteroskedasticity in that case? $\endgroup$
    – Justina
    Jun 8, 2018 at 13:19
  • $\begingroup$ heteroskedasticity is a symptom .. possible causes are multiple .. on;y your data knows for sure .. post your data and I will suggest a minimally sufficient "transformation" . That transformation could be as simple as adding a level shift , a seasonal pulse , a pulse or a local time trend.... OR incorporating weights to deal with a n error variance that changes deterministically over time OR a change in parameters over time OR a dependence of the error variance and the level of the series over time OR an error variance that changes stochastically over time. $\endgroup$
    – IrishStat
    Jun 8, 2018 at 14:21
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    $\begingroup$ @Justina, I would say, if there is conditional heteroskedasticity, why not deal with it by using a model developed specifically for conditional heteroskedasticity? ARIMA-GARCH is a simple model, I guess considerably simpler than looking for all the features IrishStat has suggested to look for. Only if ARIMA-GARCH is inadequate would I proceed that way. To paraphrase, if aspirin is what you need, why bother treating yourself with all the pills and tablets you have at home? $\endgroup$
    – Richard Hardy
    Jun 8, 2018 at 16:07
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    $\begingroup$ The side effects of over-transforming such as GARCH.ARCH need to be studiously avoided and used only when necessary. To prove the need for the GARCH complications one needs to confirm that simpler adjustments/transformations are inadequate to the task. Over complicating models is not good statistics. $\endgroup$
    – IrishStat
    Jun 8, 2018 at 19:47
  • $\begingroup$ If there is conditional heteroskedasticity, not using a model designed specifically for conditional heteroskedasticity is hard to justify. GARCH being a very simple model (GARCH(1,1) adds only two parameters to the existing model for the conditional mean), I see no objective foundation for the criticism above. $\endgroup$
    – Richard Hardy
    Jun 9, 2018 at 6:35

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