I am analysing the stock index returns data for few countries. From observation of the ACF and PACF there seem to be no significant peaks at any lags.
However, applying the auto.arima function from the forecast package yields an ARIMA(4,0,4) model. I am confused with such results as the ACF/PACF do not even show significance. The model seems to pass the portmanteau test.
I am using the Box-Jenkins approach for my project and do not know how to explain this. I wonder if any analysis is possible with no significant acf/pacf lags, and whether if I can state that ARIMA(4,0,4) is the best fitted model only considering AIC SBC etc. (for instance stating that 'although acf/pacf does not show any significant lags, but considering the possible models' AIC/SBC values of p,q<=5, ARIMA(4,0,4) model was found to be best fitted')
There does not seem to be seasonality present in my data as there was no pattern in ACF/PACF.