The Lagged Scatterplot Link

The second plot is a lagged scatterplot of fourth quarter precipitation plotted vertically and third quarter precipitation plotted horizontally. All pairs of locations up to a distance of 50000 are represented. Generally, in a static plot an analyst would first select a lag distance and then plot the lagged scatterplot for locations within a small range around the lag, but in this dynamic environment the selection of the lag is done using linked brushing. It is not only possible to mark off several lags, as we have done in this example, but also to run the brush through the lags dynamically to assess the continuous change in correlation.

Unlike in time series analysis where time is usually treated as discrete, that is, time = 0,1,2,3,..., so lags are clearly defined, space is usually continuous. Setting lags involves binning the distances. In a static environment the bandwidth of the bins needs to be selected a priori, but in this dynamic environment changing the bandwidth is synonymous with changing the rectangular brush size.

If the same variable was plotted both horizontally and vertically we would expect that the lag 0 points will all be on the y=x line. With different variables plotted horizontally than vertically, as there are here, there is no such expectation. However if the two lagged variables are highly correlated then the points would be scattered close to the y=x line. In this example the lag 0 points (red) have a weak negative correlation, that is, roughly, high precipitation in the third quarter suggests low precipitation in the fourth quarter and vice versa. Also, it appears from looking at the other two lags that there is little spatial dependence at different lags because the scatter of points at the different lags (red to orange to blue) does not change much.