[R-SIG-Finance] ARIMA,GARCH and differences

[babel at centrum.sk]

Dear friends

This is maybe trivial question for you, but why I get different results when I use return series and the original price series with 1.differences speciefied in ARIMA model? For example
x<-priceSeries
ret<-diff(log(x))
ret1<-diff(x)

fit_arma = armaFit(~ arma(5,0), data = ret)
fit_arma1 = armaFit(~ arma(5,0), data = ret1)
fit_arima = armaFit(~ arima(5,1,0), data = x)

The first model has the smallest AIC. AR parameters are very similar but not the same. 

The second question is more critical for me. Is there any possibility to enlarge  the package fGarch for the joint estiamtion of ARIMA+GARCH? Because in mean equation you can specifie only AR, MA, or ARMA model, not ARIMA. This extension I consider very important, because using the differences biult-in model,( I mean ARIMA) simplify the entire fitting and forecasting proces. If you use ARIMA, you dont need to make reverse transformation (from return to price series - from diff(log) to original scale). For evauation part it is not a big problem but for prediction part I find it difficult, therefore, I will prefer to use ARIMA so the garchFit function would produce the prediction and make the reverse transformation for me. (like the armaFit does)

Thank you very much for any suggestion you provide