ROC and Type I error rate curves for the 2D χ
2 vs DW analysis (green squares) compared to its two single constituent tests, χ
2 (red triangles) and DW (blue circles). The ROC curves (A,C) show the ability of the different tests to successfully reject the models that should be rejected (TPR), while rejecting as few as possible of the true models (FPR). In other words, a steep rise, and a high AUC is evidence of a good test. Since tests in practice only are used with p-values below 0.05, only the first part of the plot is shown (FPR <0.1). The Type I error rate plots (B,D) examine the same ability of producing correct p-values as in Figure4. However, the combination used here (2D χ
2 vs DW, green squares) does lie close to the identity line, together with the single test statistics. The upper plots, (A,B), show the results for the static example, and (C,D) for the dynamic example. As can be seen, the 2D χ
2 vs DW test is consistent (B,D) and superior to both of its constituents tests, which is evident from the greater AUC in both the static and the dynamic case (A,C).