50 CUSUM Wilcoxon α = 4 . 5 α = 6 α = 4 . 5 α = 6 H n h = 1 h = 0 . 5 h = 2 h = 1 h = 0 . 5 h = 2 h = 1 h = 0 . 5 h = 2 h = 1 h = 0 . 5 h = 2 τ = 0 . 25 0.6 500 0.464 0.252 0.963 0.467 0.270 0.978 0.119 0.925 0.937 0.130 0.929 0.929 1000 0.589 0.383 0.995 0.596 0.385 0.997 0.112 0.994 0.995 0.118 0.995 0.996 2000 0.708 0.529 1.000 0.694 0.574 1.000 0.108 1.000 1.000 0.104 1.000 1.000 0.7 500 0.330 0.164 0.852 0.330 0.174 0.882 0.078 0.584 0.587 0.078 0.606 0.591 1000 0.374 0.197 0.937 0.404 0.207 0.961 0.066 0.781 0.784 0.068 0.781 0.780 2000 0.431 0.263 0.983 0.443 0.273 0.991 0.060 0.932 0.929 0.061 0.934 0.936 0.8 500 0.235 0.116 0.670 0.244 0.111 0.686 0.074 0.314 0.328 0.074 0.332 0.319 1000 0.258 0.131 0.770 0.256 0.132 0.786 0.067 0.398 0.386 0.067 0.398 0.382 2000 0.275 0.139 0.837 0.271 0.137 0.861 0.060 0.502 0.499 0.059 0.505 0.501 0.9 500 0.179 0.088 0.470 0.170 0.084 0.486 0.088 0.251 0.254 0.088 0.252 0.262 1000 0.184 0.100 0.513 0.177 0.097 0.523 0.078 0.267 0.277 0.079 0.272 0.272 2000 0.191 0.101 0.564 0.191 0.099 0.566 0.072 0.283 0.283 0.065 0.279 0.277 τ = 0 . 5 0.6 500 0.377 0.954 0.417 0.967 0.988 0.990 0.990 0.990 1000 0.565 0.992 0.594 0.996 1.000 1.000 1.000 1.000 2000 0.774 0.999 0.814 0.999 1.000 1.000 1.000 1.000 0.7 500 0.252 0.821 0.252 0.839 0.808 0.808 0.806 0.809 1000 0.313 0.932 0.333 0.946 0.934 0.937 0.936 0.935 2000 0.416 0.984 0.436 0.987 0.992 0.992 0.990 0.991 0.8 500 0.170 0.623 0.166 0.651 0.529 0.525 0.515 0.528 1000 0.196 0.733 0.199 0.757 0.605 0.615 0.624 0.631 2000 0.226 0.838 0.230 0.848 0.741 0.738 0.746 0.734 0.9 500 0.127 0.440 0.132 0.445 0.410 0.419 0.404 0.406 1000 0.137 0.487 0.140 0.506 0.442 0.440 0.452 0.424 2000 0.135 0.542 0.148 0.540 0.466 0.467 0.468 0.473 Table 8: Rejection rates of the CUSUM and Wilcoxon test for LMSV time series of length n with Hurst parameter H , tail index α and a shift in the variance of height h 2 after a proportion τ . The calculations are based on 5,000 simulation runs.