Poincaré Plots for Residual Analysis

After some suitable ordering of the residuals, et, t = 1, . . . , n, it is suggested that scatter plots of et+1 vs. et along with a robust smooth loess trend be routinely examined to check for lack of statistical independence. Such plots may be termed Poincaré plots because of their similarity to plots used in nonlinear dynamical systems. Poincaré plots are helpful in detecting positive correlations in the fitted model which may invalidate statistical inferences. Poincaré plots are common in time series analysis but do not appear to be frequently used in other situations.