49 Table 7: Rejection rates of the self-normalized CUSUM and the self-normalized Wilcoxon test for LMSV time series (Pareto distributed ε$_{j}$, j ≥ 1) of length n with Hurst parameter H , tail index α and a shift in the mean of height h after a proportion τ . The calculations are based on 5,000 simulation runs. self-norm. CUSUM self-norm. Wilcoxon α = 2 . 5 α = 4 α = 2 . 5 α = 4 H n h = 0 h = 0 . 5 h = 1 h = 0 h = 0 . 5 h = 1 h = 0 h = 0 . 5 h = 1 h = 0 h = 0 . 5 h = 1 τ = 0 . 25 0.6 500 0.046 0.181 0.539 0.042 0.688 0.958 0.032 0.879 0.991 0.030 0.995 1.000 1000 0.049 0.290 0.722 0.044 0.862 0.990 0.032 0.973 1.000 0.030 1.000 1.000 2000 0.053 0.458 0.875 0.026 0.967 0.999 0.034 0.999 1.000 0.028 1.000 1.000 0.7 500 0.051 0.204 0.552 0.042 0.697 0.954 0.029 0.680 0.938 0.021 0.960 0.997 1000 0.050 0.295 0.727 0.046 0.866 0.990 0.032 0.856 0.988 0.027 0.993 1.000 2000 0.049 0.455 0.868 0.042 0.966 0.998 0.037 0.948 0.999 0.030 0.999 1.000 0.8 500 0.045 0.226 0.580 0.044 0.720 0.951 0.031 0.424 0.772 0.021 0.815 0.964 1000 0.042 0.338 0.736 0.040 0.870 0.989 0.033 0.559 0.862 0.024 0.915 0.984 2000 0.050 0.498 0.881 0.052 0.960 0.998 0.034 0.673 0.938 0.023 0.958 0.998 0.9 500 0.044 0.329 0.645 0.041 0.760 0.947 0.031 0.309 0.582 0.020 0.640 0.861 1000 0.051 0.446 0.761 0.042 0.871 0.980 0.039 0.369 0.650 0.034 0.734 0.912 2000 0.041 0.585 0.869 0.048 0.949 0.996 0.049 0.422 0.719 0.039 0.791 0.947 τ = 0 . 5 0.6 500 0.384 0.801 0.904 0.990 0.994 1.000 1.000 1.000 1000 0.564 0.909 0.973 0.998 1.000 1.000 1.000 1.000 2000 0.744 0.962 0.993 1.000 1.000 1.000 1.000 1.000 0.7 500 0.401 0.801 0.902 0.989 0.950 1.000 1.000 1.000 1000 0.565 0.904 0.972 0.998 0.993 1.000 1.000 1.000 2000 0.744 0.966 0.994 0.999 1.000 1.000 1.000 1.000 0.8 500 0.424 0.804 0.899 0.990 0.776 0.977 0.987 0.999 1000 0.589 0.905 0.966 0.997 0.896 0.995 0.998 1.000 2000 0.761 0.959 0.994 0.999 0.963 0.999 1.000 1.000 0.9 500 0.527 0.815 0.893 0.982 0.622 0.890 0.912 0.990 1000 0.650 0.898 0.959 0.997 0.708 0.936 0.956 0.996 2000 0.781 0.954 0.989 0.999 0.779 0.960 0.976 0.998