advanced-algorithmic-trading

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9.3.2 Correlogram
We can also plot the correlogram of a DWN using R, see Figure 9.1. Firstly we’ll set the random
seed to be 1, so that your random draws will be identical to mine. Then we will sample 1000
elements from a normal distribution and plot the autocorrelation:
> set.seed(1)
> acf(rnorm(1000))
Figure 9.1: Correlogram of Discrete White Noise.
Notice that at k = 6, k = 15 and k = 18, we have three peaks that differ from zero at the 5%
level. However, this is to be expected simply due to the variation in sampling from the normal
distribution.
Once again, we must be extremely careful in our interpretation of results. In this instance,
do we really expect anything physically meaningful to be happening at k = 6, k = 15 or k = 18?
Notice that the DWN model only has a single parameter, namely the variance σ 2 . Thankfully,
it is straightforward to estimate the variance with R. We can simply use the var function:
> set.seed(1)
> var(rnorm(1000, mean=0, sd=1))
[1] 1.071051
We have specifically highlighted that the normal distribution above has a mean of zero and a
standard deviation of 1 (and thus a variance of 1). R calculates the sample variance as 1.071051,
which is close to the population value of 1.
The key takeaway with Discrete White Noise is that we use it as a model for the residuals.
We are looking to fit other time series models to our observed series, at which point we use DWN