Figure A1.

Empirical values of CEofOP statistics $\frac{1}{L}\underset{\theta \in (0,1)}{max}\mathrm{CEofOP}\left(\lfloor \theta L\rfloor ;{\pi }^{d,L}\right)$ converge to the theoretical values ${\mathsf{\Delta }}_{0.5,0.5}^d$ for autoregressive processes as L increases for $d=1$ (a) and $d=2$ (b). Here, AR, ${\varphi }_1\to {\varphi }_2$ stands for the process $\mathrm{AR}\left(({\varphi }_1,{\varphi }_2),L/2\right)$. The provided empirical values are obtained either as 5th percentile (for ${\varphi }_1\ne {\varphi }_2$) or as 95th percentile (for ${\varphi }_1={\varphi }_2$) from 1000 trials.