advanced-algorithmic-trading

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autocorrelation:
> layout(1:2)
> acf(z)
> acf(diff(z))
Figure 12.2: Correlograms of z t and the differenced series of z t
Hence this realisation of z t clearly looks like a random walk. The next step is to create x t
and y t from z t , using p = 0.3 and q = 0.6, and then plot both:
> x <- y <- rep(0, 1000)
> x <- 0.3*z + rnorm(1000)
> y <- 0.6*z + rnorm(1000)
> layout(1:2)
> plot(x, type="l")
> plot(y, type="l")
As you can see they both look similar. Of course they will be by definition–they share the
same underlying random walk structure from z t . We can now form the linear combination, comb,
using p = 2 and q = −1 and examine the autocorrelation structure:
> comb <- 2*x - y
> layout(1:2)
> plot(comb, type="l")
> acf(comb)
It is clear that the combination series comb looks very much like a stationary series. This is
to be expected given its definition.