I am trying to implement ARIMA(4,0,4) - GARCH (P,Q) model in Python (the ARIMA orders were selected based on best AIC/BIC). Multiple sources suggest fitting ARIMA and GARCH simultaneously rather than serially (meaning fitting best ARIMA first and then fitting GARCH on residuals) is the right way - here is one of them.
The only Python package I found for this purpose is arch, however, for the mean model it only has following options:
Zero mean (ZeroMean) - useful if using residuals from a model estimated separately
Constant mean (ConstantMean) - common for most liquid financial
Autoregressive (ARX) with optional exogenous regressors
Heterogeneous (HARX) autoregression with optional exogenous
Exogenous regressors only (LS)
So no option for ARIMA mean. Is there any package for simultaneous fitting ARIMA - GARCH model in Python?
Thanks in advance!