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?
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
- 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.