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Figure 11.2: Correlogram of the residuals of the fitted ARIMA(1,1,1) model
Box-Ljung test
data: resid(x.arima)
X-squared = 19.0413, df = 20, p-value = 0.5191
We can see that the p-value is significantly larger than 0.05 and as such we can state that
there is strong evidence for discrete white noise being a good fit to the residuals. Thus the
ARIMA(1,1,1) model is a good fit as expected.
11.2.4 Financial Data and Prediction
In this section we are going to fit ARIMA models to Amazon, Inc. (AMZN) and the S&P500
US Equity Index (^GPSC, in Yahoo Finance). We will make use of the forecast library, written
by Rob J Hyndman[54].
We can go ahead and install the library in R:
> install.packages("forecast")
> library(forecast)
Now we can use quantmod to download the daily price series of Amazon from the start of
2013. Since we will have already taken the first order differences of the series, the ARIMA fit
carried out shortly will not require d > 0 for the integrated component:
> require(quantmod)
> getSymbols("AMZN", from="2013-01-01")