advanced-algorithmic-trading

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Figure 8.2: Correlogram plotted in R of a sequence of normally distributed random variables.
8.5.1 Example 1 - Fixed Linear Trend
The following R code generates a sequence of integers from 1 to 100 and then plots the autocorrelation:
> w <- seq(1, 100)
> acf(w)
The plot is displayed in Figure 8.3.
Notice that the ACF plot decreases in an almost linear fashion as the lags increase. Hence a
correlogram of this type is clear indication of a trend.
8.5.2 Example 2 - Repeated Sequence
The following R code generates a repeated sequence of numbers with period p = 10 and then
plots the autocorrelation:
> w <- rep(1:10, 10)
> acf(w)
The plot is displayed in Figure 8.4.
We can see that at lag 10 and 20 there are significant peaks. This makes sense, since the
sequences are repeating with a period of 10. Interestingly, note that there is a negative correlation
at lags 5 and 15 of exactly -0.5. This is very characteristic of seasonal time series and behaviour
of this sort in a correlogram is usually indicative that seasonality/periodic effects have not fully
been accounted for in a model.