advanced-algorithmic-trading

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Figure 10.17: Residuals of MA(2) Model Fitted to S&P500 Daily Log Prices
sigma^2 estimated as 0.0001838: log likelihood = 6253.9, aic = -12497.81
10.18.
Finally we can make a plot of the residuals of this fitted MA(3) model as given in Figure
> acf(gspcrt.ma$res[-1])
This is precisely what we see in the correlogram of the residuals. Hence the MA(3) as with
the other models above is not a good fit for the S&P500.
10.5.6 Next Steps
We have now examined two major time series models in detail, namely the Autogressive model
of order p, AR(p) and then Moving Average of order q, MA(q). We have seen that they are both
capable of explaining away some of the autocorrelation in the residuals of first order differenced
daily log prices of equities and indices, but volatility clustering and long-memory effects persist.
It is finally time to turn our attention to the combination of these two models, namely the
Autoregressive Moving Average of order p, q, ARMA(p,q) to see if it will improve the situation
any further.