advanced-algorithmic-trading

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> ft <- as.numeric(ftrt)
> ft <- ft[!is.na(ft)]
The next task is to fit a suitable ARIMA(p,d,q) model. We saw how to do that in the previous
chapter so the procedure will not be repeated here. Instead the code will simply be provided:
> ftfinal.aic <- Inf
> ftfinal.order <- c(0,0,0)
> for (p in 1:4) for (d in 0:1) for (q in 1:4) {
> ftcurrent.aic <- AIC(arima(ft, order=c(p, d, q)))
> if (ftcurrent.aic < ftfinal.aic) {
> ftfinal.aic <- ftcurrent.aic
> ftfinal.order <- c(p, d, q)
> ftfinal.arima <- arima(ft, order=ftfinal.order)
> }
> }
Since we have already differenced the FTSE returns once we should expect our integrated
component d to equal zero, which it does:
> ftfinal.order
[1] 4 0 4
Thus we receive an ARIMA(4,0,4) model. This contains four autoregressive parameters and
four moving average parameters.
We are now in a position to decide whether the residuals of this model fit possess evidence
of conditional heteroskedastic behaviour. To test this we need to plot the correlogram of the
residuals, as given in Figure 11.10.
> acf(resid(ftfinal.arima))
This looks like a realisation of a discrete white noise process indicating that we have achieved
a good fit with the ARIMA(4,0,4) model.
To test for conditional heteroskedastic behaviour we need to square the residuals and plot
the corresponding correlogram, as given in Figure 11.11.
> acf(resid(ftfinal.arima)^2)
We can see clear evidence of serial correlation in the squared residuals, leading us to the
conclusion that conditional heteroskedastic behaviour is present in the diff log return series of
the FTSE100.
We are now in a position to fit a GARCH model using the tseries library.
The first command actually fits an appropriate GARCH model, with the trace=F parameter
telling R to suppress excessive output.
The second command removes the first element of the residuals, since it is NA:
> ft.garch <- garch(ft, trace=F)
> ft.res <- ft.garch$res[-1]
To test for a good fit we can plot the correlogram of the GARCH residuals and the square
GARCH residuals as given in Figure 11.12.
> acf(ft.res)