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")

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 ?



To answer your title question, your specifications are not the same: in ugarchspec you use a normal distribution for the standardized innovations (distribution.model = "norm"), while in garchFit you use a Student distribution (cond.dist = 'std'). No wonder the estimated coefficients are not the same.

For the remaining questions, I suggest posting them one by one rather than all in the same thread.

  • $\begingroup$ Ok, thank you ! a very avoidable mistake. Wouldn't it be a bit spammy since they are quite close ? $\endgroup$ – quezac Feb 3 '20 at 19:44
  • $\begingroup$ @quezac, well, the ones that are close can stay together, but I think a couple distinct ones can be identified. You would probably not even need to ask them as there are some similar threads with answers already. $\endgroup$ – Richard Hardy Feb 3 '20 at 20:36

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