What is the time plot of the series like? What is the correlogram like? Maybe it was not necessary to fit a Garch(1,1) model. Rather than removing the ARMA model maybe it is necessary to remove the GARCH model. It is necessary that the model be both stationary and invertible for forecasting purpose.

The arma has been fitted on the stock returns to account for serial correlation in stock returns. The correlogram of the residuals indicate that there is serial correlation in daily stock returns and that the serial correlation is removed by applying the arma(3,3). I test for arch effects using Engle LM test and find that there are arch effects. I add ARCH, GARCH, EGARCH and GJR-GARCH. EGARCH is fine but the other 3 make the arma equation noninvertible and nonstationary. I want to forecast volatility out-of-sample.

Hi,

I think that you need to reconsider your ARMA structure. See whether seasonality is present in the data. If it is the case you may need to incorporate Seasonal AR and Seasonal MA or seasonal dummies to control for the seasonality. You need to use the ACF and PACF of the stationary variable to find the relevant ARMA structure. If you are using EViews to estimate, there is a good feature that will help you to identify the relevant ARMA structure, that is "Automatic ARIMA Forecasting".  This is available in Eviews 9. 

Good Luck.

Thushara

Hi! 

The ARIMA has been identified using AIC. I am using eviews 7. I have tried using the auto arima in E9 and I get the same result, an arima(3,3). The problem is the non invertibility condition and non stationarity. 

I don't have access to a recent version of Eviews. I would estimate a selection of ARIMA(p,d,q) Garch(1,1) models and then select p, d, and q on the basis of the information criteria for the combined models rather than that of an ARIMA(p,d,d) model.

If your ARIMA model is non-stationary then you can not use it. Is your original series non-stationary? Perhaps you need to difference it again. You do not mention what your series is. Are there periodic components. ARMA models are simply a way of approximating the dynamics of a stationary process. In real applications have never encountered what could be described as a true model - only an approximation.

I have used the fGarch and rugarch packages in R to select and estimate models such as these.

Dear @S.C Thushara

If I want to estimate ARIMAx by add four exogenous variables, whether the lag p d and q of ARIMA can estimate by "Automatic ARIMA Forecasting" in Eviews 9?

Thanks!

yes you can. you need to include those exogenous variables when using automatic arima forecasting. However, if the arima model fits the data well, there is a possibility that your exogenous variables would be insignificant.

Kind regards

Thushara