advanced-algorithmic-trading

115
[1] 0.440208 0.764392
We can see that the 95% confidence interval contains the true parameter value of β 1 = 0.6
and so we can judge the model a good fit. Obviously this should be expected since we simulated
the data in the first place.
How do things change if we modify the sign of β 1 to -0.6? We can perform the same analysis:
> set.seed(1)
> x <- w <- rnorm(100)
> for (t in 2:100) x[t] <- w[t] - 0.6*w[t-1]
> layout(1:2)
> plot(x, type="l")
> acf(x)
The output is given in Figure 10.11.
Figure 10.11: Realisation of MA(1) Model, with β 1 = −0.6 and Associated Correlogram
We can see that at k = 1 we have a significant peak in the correlogram, except that it shows
negative correlation, as we would expect from a MA(1) model with negative first coefficient.
Once again all peaks beyond k = 1 are insignificant. Let us fit a MA(1) model and estimate the
parameter:
> x.ma <- arima(x, order=c(0, 0, 1))
> x.ma
Call:
arima(x = x, order = c(0, 0, 1))