advanced-algorithmic-trading

120
> amznrt.ma
Call:
arima(x = amznrt, order = c(0, 0, 3))
Coefficients:
ma1 ma2 ma3 intercept
-0.0262 -0.0690 0.0177 0.0012
s.e. 0.0214 0.0217 0.0212 0.0005
sigma^2 estimated as 0.0007009: log likelihood = 4801.37, aic = -9592.75
Once again, we can plot the residuals, as given in Figure 10.15.
> acf(amznrt.ma$res[-1])
Figure 10.15: Residuals of MA(3) Model Fitted to AMZN Daily Log Prices
The MA(3) residuals plot looks almost identical to that of the MA(2) model. This is not
surprising as we are adding a new parameter to a model that has seemingly explained away much
of the correlations at shorter lags, but that won’t have much of an effect on the longer term lags.
All of this evidence is suggestive of the fact that an MA(q) model is unlikely to be useful in
explaining all of the serial correlation in isolation, at least for AMZN.
S&P500
If you recall in the previous section we saw that the first order differenced daily log returns
structure of the S&P500 possessed many significant peaks at various lags, both short and long.