advanced-algorithmic-trading

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10.4.4 Simulations and Correlograms
AR(1)
Let us begin with an AR(1) process. This is similar to a random walk, except that α 1 does
not have to equal unity. Our model is going to have α 1 = 0.6. The R code for creating this
simulation is given as follows:
> set.seed(1)
> x <- w <- rnorm(100)
> for (t in 2:100) x[t] <- 0.6*x[t-1] + w[t]
Notice that our for loop is carried out from 2 to 100, not 1 to 100, as x[t-1] when t = 0 is
not indexable. Similarly for higher order AR(p) processes, t must range from p to 100 in this
loop.
We can plot the realisation of this model and its associated correlogram using the layout
function, given in Figure 10.1.
> layout(1:2)
> plot(x, type="l")
> acf(x)
Figure 10.1: Realisation of AR(1) Model, with α 1 = 0.6 and Associated Correlogram.
We can now try fitting an AR(p) process to the simulated data that we have just generated
to see if we can recover the underlying parameters. You may recall that we carried out a similar
procedure in the previous chapter on white noise and random walks.
R provides a useful command ar to fit autoregressive models. We can use this method to
firstly tell us the best order p of the model (as determined by the AIC above) and provide us