> final.aic #-535902.3  -535902.3 > final.order #3 0 0  3 0 0 > Box.test(resid(final.arma), lag=20, type="Ljung-Box") #X-squared = 26.275, df = 20, p-value = 0.1569 Box-Ljung test data: resid(final.arma) X-squared = 26.275, df = 20, p-value = 0.1569
the $p$-value is greater than 0.05 and as such we CAN say that the residuals are a realisation of discrete white noise. Hence the autocorrelation in the residuals that is explained by the fitted ARMA model.
Box.test(resid(ftfinal.arima)^2, lag=20, type="Ljung-Box") #p-value < 2.2e-16 so correlation present?
IF there is evidence of serial correlation in the squared residuals, conclude that conditional heteroskedasticity is present in the original series.
So my results seem to imply that:
- the autocorrelation in the model is explained by ARMA(3,0,0).... Would a GARCH model even add anything then?;
- there IS regular variability (heteroskedasticity) being explained by the GARCH model.
So if I use a model with ARMA+GARCH it will explain more variance (and therefore predict better) than the two models individually?