How to solve the problem of errors autocorrelation in ARMA model? What is the fastest way to find the best fit ARMA model?

Hey I am writing thesis on time series, but the ARMA model that I created seems doesn't work perfectly. For example I got an ARMA(1,1) model for Nikkei 225, however when I test the model errors, it still have auto-correlation for the 1st lag.

Does anyone know how to solve the problem of errors autocorrelation in ARMA model? What is the fastest way to find the best fit ARMA model?

Thanks a lot!

Answer 1

[Roger Wohlwend]

To remove the autocorrelation you have to add more AR or MA terms. It is strange that you still have first-order autocorrelation in your ARMA(1,1) model. Are you working with stationary data? I hope you are. If you are not that could explain the autocorrelation.

The fastest way to find the best fit? People often use an information criterion to find the best model. You will find extensive information on that in the Matlab documention.

If your goal is forecasting the Nikkei 225 index, then an ARMA model may not be an appropriate model. For financial data the predictive power of ARMA models is in general quite low.

[Zihao]

Thanks a lot Roger! I am using the daily log returns of the indexes (SP500, FTSE100, DAX index and Nikkei 225). So you mean I should use a GARCH model or other kinds of models to fit? My goal is to study the volatility and skewness transmissions.

[Roger Wohlwend]

Using daily log returns is perfect. If you want to study volatilty then you should indeed do a GARCH model because ARMA models assume that volatility is constant.