advanced-algorithmic-trading

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> amzn = diff(log(Cl(AMZN)))
As in the previous chapter we are now going to loop through the combinations of p, d and
q, to find the optimal ARIMA(p,d,q) model. By "optimal" we mean the order combination that
minimises the Akaike Information Criterion (AIC):
> azfinal.aic <- Inf
> azfinal.order <- c(0,0,0)
> for (p in 1:4) for (d in 0:1) for (q in 1:4) {
> azcurrent.aic <- AIC(arima(amzn, order=c(p, d, q)))
> if (azcurrent.aic < azfinal.aic) {
> azfinal.aic <- azcurrent.aic
> azfinal.order <- c(p, d, q)
> azfinal.arima <- arima(amzn, order=azfinal.order)
> }
> }
We can see that an order of p = 4, d = 0, q = 4 was selected. Notably d = 0, as we have
already taken first order differences above:
> azfinal.order
[1] 4 0 4
If we plot the correlogram of the residuals we can see if we have evidence for a discrete white
noise series, see Figure 11.3.
> acf(resid(azfinal.arima), na.action=na.omit)
There are two significant peaks, namely at k = 15 and k = 21, although we should expect
to see statistically significant peaks simply due to sampling variation 5% of the time. Let us
perform a Ljung-Box test and see if we have evidence for a good fit:
> Box.test(resid(azfinal.arima), lag=20, type="Ljung-Box")
Box-Ljung test
data: resid(azfinal.arima)
X-squared = 12.6337, df = 20, p-value = 0.8925
As we can see the p-value is greater than 0.05 and so we have evidence for a good fit at the
95% level.
We can now use the forecast command from the forecast library in order to predict 25 days
ahead for the returns series of Amazon, which is provided in Figure 11.4.
> plot(forecast(azfinal.arima, h=25))
We can see the point forecasts for the next 25 days with 95% (dark blue) and 99% (light
blue) error bands. We will be using these forecasts in our first time series trading strategy when
we come to combine ARIMA and GARCH later in the book.
Let us carry out the same procedure for the S&P500. Firstly we obtain the data from
quantmod and convert it to a daily log returns stream: