The index plot is often used when plotting distance measures such as Mahalanobi’s distance or Hadi’s distance. Each observation has a line drawn from it’s value to zero. This creates a series of vertical lines. Using time series as the x-axis, then dips or gaps or peaks in the sequence of verticle lines reveals places where something interesting may be happening in that time series.
Experiment with this plot in which the y and x are the residuals and the predicted values from a regression or linear model. You may be surprised with the patterns revealed.