I have selected the best ARIMA(p,d,q) model via maximisation of AIC and got the estimates of its AR & MA coefficients.
However, after having subsequently modelled the conditional volatility with a GARCH(1,1) via
rugarch package in $R$ (and having previously specified to consider ARMA(5,5) for conditional mean) the estimates for conditional mean comes out to be different!
- Is it normal? Why just adding a model for conditional variance I'm affecting the conditional mean model?
- Should I force
rugarchto use the the same estimates I got before by modelling just the residuals of the ARMA(5,5) model with GARCH? Would I get "better estimates" or not?