I have financial time series with non constant variance. I suppose that using ARMA- GARCH i will create more accurate confident intervals for predictions than using ARMA model. This is how i fit model 1. Turn to log returns from original series. (It becomes stationary)
Select appropriate ARMA model by AIC.
Testing residual for ARCH effect using LM test. (Rejects null hypothesis - there is arch effect)
Select appropriate GARCH(p,q) using AIC.
a) So my question is how should i combine this models to create mean_forecast and confidence interval?
b) Here https://stats.stackexchange.com/a/143521/180509 @Richard Hardy suggests to determine both the ARMA and the GARCH parts simultaneously. How i can do it simultaneously and how it implement it in python? Thanks