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Figure 10.16: Residuals of MA(1) Model Fitted to S&P500 Daily Log Prices
-0.1189 -0.0524 2e-04
s.e. 0.0216 0.0223 2e-04
sigma^2 estimated as 0.0001839: log likelihood = 6252.96, aic = -12497.92
Once again we can make a plot of the residuals of this fitted MA(2) model as given in Figure
10.17.
> acf(gspcrt.ma$res[-1])
While the peak at k = 2 has disappeared (as we would expect) we are still left with the
significant peaks at many longer lags in the residuals. Once again we find the MA(2) model is
not a good fit.
We should expect for the MA(3) model to see less serial correlation at k = 3 than for the
MA(2). We should also expect no reduction in further lags.
> gspcrt.ma <- arima(gspcrt, order=c(0, 0, 3))
> gspcrt.ma
Call:
arima(x = gspcrt, order = c(0, 0, 3))
Coefficients:
ma1 ma2 ma3 intercept
-0.1189 -0.0529 0.0289 2e-04
s.e. 0.0214 0.0222 0.0211 3e-04