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?
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1$\begingroup$ Typically, there isn't enough monthly data to estimate a reasonable ARMA-GARCH model. However, if one can trust certain aspects of certain previous studies, estimation can be achieved in a Bayesian fashion. More generally, some form of regularization can be applied. $\endgroup$– stansSep 11 at 7:11
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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.
