When ARMA-GARCH Models Make Sense for Monthly Financial Data

Summary

The document asks whether ARMA-GARCH models are inappropriate for monthly observations and what alternatives might be used. The answer says there is no technical prohibition: ARCH was originally applied to quarterly inflation data. The more important questions are whether mean dependence and volatility clustering are detectable at a given sampling frequency and whether those patterns matter for the subject being studied.

For monthly stock returns, momentum is offered as a reason ARMA structure may be relevant. The answer is less certain about monthly volatility clustering, suggesting it may be weaker than at daily frequency. It points to a review of empirical return properties that discusses clustering in daily and sometimes weekly data, without establishing a general monthly result. The response does not recommend specific alternative models or provide a systematic comparison, so model choice remains an empirical and subject-specific decision.

Key ideas

• There is no technical rule that prevents fitting ARMA-GARCH models to monthly data.
• ARCH methods were initially used on quarterly inflation observations.
• Whether monthly data exhibit meaningful autocorrelation or volatility clustering is an empirical question.
• Stock return momentum may make ARMA components relevant at monthly frequency.
• The answer is uncertain about monthly volatility clustering and does not prescribe alternative models.

Tags

# Are ARMA-GARCH-type models suitable for monthly data?


# Are ARMA-GARCH-type models suitable for monthly data?












I understand that ARMA-GARCH models and their variations are usually applied to daily time series. While I know that such models can be also estimated on monthly data, I have seen few applications in the literature. Is there a specific reasons why such models are not common for monthly data? If so, which kind of models (for the mean and the volatility) can be used, in general as alternative?

## Answer by Richard Hardy (score 1)

https://quant.stackexchange.com/a/76585

Technically there is no reason to avoid ARMA-GARCH for low-frequency (e.g. monthly) data. When Robert Engle introduced the ARCH model in 1982, his application was on quarterly data of inflation.

Different but no less important questions are

- whether ARMA and GARCH patterns in monthly data are statistically prominent

and/or

- whether they are interesting from the subject-matter perspective.

Regarding 1., the phenomenon of momentum in stock prices suggests ARMA can be relevant. I am not sure if volatility clustering is prominent in monthly stock returns; I suppose not as much as for daily ones. Cont "Empirical properties of asset returns: stylized facts and statistical issues" (2001) mentions volatility clustering in daily and sometimes weekly data but he stops there.

Regarding 2., I do not know.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.