I'm trying to forecast the CAC40, I get my ARIMA(4, 1 ,5) (with two non-significative parameters) model using the differents information criterion and correlograms. After testing the residuals I see that I need to add some GARCH effects, so I go for a GARCH(1, 1) and the residuals are fixed.
The problem is here, I want to predict it so I use :
garch11 <- ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(4, 5), include.mean = TRUE), distribution.model = "norm") garchfit <- ugarchfit(spec = garch11, data = lcac.ret, solver = "hybrid") garchfit
I get totally different results and parameters. And it's not the best model since if I try the same code with, let's say, ARIMA(3, 1, 3) I get better results (more significative parameters, and lower AIC).
So I don't know what to do since there is no reason I should switch back to an ARIMA(3, 1 ,3) after the previous analyzes, and is this normal ? Why does it differs so much ?
And when I try with :
model=garchFit(~arma(4,5)+garch(1,1), data=lcac.ret, trace=F, cond.dist ='std')
I get again different results, how to explain this ?