advanced-algorithmic-trading

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We fit an ARIMA model by looping over the values of p, d and q:
> spfinal.aic <- Inf
> spfinal.order <- c(0,0,0)
> for (p in 1:4) for (d in 0:1) for (q in 1:4) {
> spcurrent.aic <- AIC(arima(sp, order=c(p, d, q)))
> if (spcurrent.aic < spfinal.aic) {
> spfinal.aic <- spcurrent.aic
> spfinal.order <- c(p, d, q)
> spfinal.arima <- arima(sp, order=spfinal.order)
> }
> }
The AIC tells us that the "best" model is the ARIMA(2,0,1) model. Notice once again that
d = 0, as we have already taken first order differences of the series:
> spfinal.order
[1] 2 0 1
We can plot the residuals of the fitted model to see if we have evidence of discrete white
noise, see Figure 11.5.
> acf(resid(spfinal.arima), na.action=na.omit)
Figure 11.5: Correlogram of residuals of ARIMA(2,0,1) model fitted to S&P500 daily log returns
The correlogram looks promising, so the next step is to run the Ljung-Box test and confirm
that we have a good model fit: