## 2.7 Lag plots

Figure 2.13 displays scatterplots of quarterly Australian beer production, where the horizontal axis shows lagged values of the time series. Each graph shows $$y_{t}$$ plotted against $$y_{t-k}$$ for different values of $$k$$.

beer2 <- window(ausbeer, start=1992)
gglagplot(beer2)

Here the colours indicate the quarter of the variable on the vertical axis. The lines connect points in chronological order. The relationship is strongly positive at lags 4 and 8, reflecting the strong seasonality in the data. The negative relationship seen for lags 2 and 6 occurs because peaks (in Q4) are plotted against troughs (in Q2)

The window() function used here is very useful when extracting a portion of a time series. In this case, we have extracted the data from ausbeer, beginning in 1992.