2.7 Lag plots

Figure 2.13 displays scatterplots of quarterly Australian beer production (we introduced in Figure 1.1), 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 \(k\).

Lagged scatterplots for quarterly beer production.

Figure 2.13: Lagged scatterplots for quarterly beer production.

Here the colours indicate the quarter of the variable on the vertical axis. 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 filter() function used here is very useful when extracting a portion of a time series. In this case, we have extracted the data from aus_production, beginning in 1992.