26 Table 2: Rejection rates of CUSUM and Wilcoxon tests 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 = 0 . 5. The calculations are based on 5,000 simulation runs. CUSUM 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 non-self-normalized 0.6 500 0.035 0.048 0.213 0.047 0.866 1.000 0.628 1.000 1.000 0.802 1.000 1.000 1000 0.034 0.085 0.745 0.051 0.993 1.000 0.578 1.000 1.000 0.751 1.000 1.000 2000 0.034 0.288 0.986 0.048 1.000 1.000 0.524 1.000 1.000 0.713 1.000 1.000 0.7 500 0.035 0.050 0.209 0.053 0.864 1.000 0.331 1.000 1.000 0.475 1.000 1.000 1000 0.037 0.087 0.752 0.058 0.994 1.000 0.270 1.000 1.000 0.384 1.000 1.000 2000 0.039 0.285 0.983 0.051 1.000 1.000 0.207 1.000 1.000 0.300 1.000 1.000 0.8 500 0.045 0.055 0.207 0.073 0.879 1.000 0.191 0.974 1.000 0.273 1.000 1.000 1000 0.041 0.108 0.757 0.066 0.994 1.000 0.144 0.994 1.000 0.187 1.000 1.000 2000 0.042 0.280 0.983 0.066 1.000 1.000 0.108 1.000 1.000 0.132 1.000 1.000 0.9 500 0.057 0.069 0.191 0.080 0.901 1.000 0.188 0.863 0.984 0.232 0.995 1.000 1000 0.059 0.111 0.783 0.090 0.992 1.000 0.139 0.888 0.990 0.165 0.996 1.000 2000 0.064 0.238 0.984 0.092 1.000 1.000 0.108 0.917 0.996 0.121 0.998 1.000 self-normalized 0.6 500 0.046 0.384 0.801 0.042 0.904 0.990 0.032 0.994 1.000 0.030 1.000 1.000 1000 0.049 0.564 0.909 0.044 0.973 0.998 0.032 1.000 1.000 0.030 1.000 1.000 2000 0.053 0.744 0.962 0.026 0.993 1.000 0.034 1.000 1.000 0.028 1.000 1.000 0.7 500 0.051 0.401 0.801 0.042 0.902 0.989 0.029 0.950 1.000 0.021 1.000 1.000 1000 0.050 0.565 0.904 0.046 0.972 0.998 0.032 0.993 1.000 0.027 1.000 1.000 2000 0.049 0.744 0.966 0.042 0.994 0.999 0.037 1.000 1.000 0.030 1.000 1.000 0.8 500 0.045 0.424 0.804 0.044 0.899 0.990 0.031 0.776 0.977 0.021 0.987 0.999 1000 0.042 0.589 0.905 0.040 0.966 0.997 0.033 0.896 0.995 0.024 0.998 1.000 2000 0.050 0.761 0.959 0.052 0.994 0.999 0.034 0.963 0.999 0.023 1.000 1.000 0.9 500 0.044 0.527 0.815 0.041 0.893 0.982 0.031 0.622 0.890 0.020 0.912 0.990 1000 0.051 0.650 0.898 0.042 0.959 0.997 0.039 0.708 0.936 0.034 0.956 0.996 2000 0.041 0.781 0.954 0.048 0.989 0.999 0.049 0.779 0.960 0.039 0.976 0.998