47 Table 5: Rejection rates of the CUSUM tests for LMSV time series (standard normal ε$_{j}$, j ≥ 1) of length n with Hurst parameter H and a shift in the mean of height h after a proportion τ . The calculations are based on 5,000 simulation runs. CUSUM self-norm. CUSUM H n h = 0 h = 0 . 5 h = 1 h = 2 h = 0 h = 0 . 5 h = 1 h = 2 τ = 0 . 25 0.6 500 0.046 0.214 0.803 1.000 0.043 0.201 0.597 0.951 1000 0.045 0.452 0.987 1.000 0.047 0.352 0.818 0.996 2000 0.043 0.816 1.000 1.000 0.044 0.575 0.957 1.000 0.7 500 0.064 0.222 0.792 1.000 0.044 0.223 0.594 0.951 1000 0.056 0.461 0.989 1.000 0.044 0.361 0.823 0.993 2000 0.050 0.815 1.000 1.000 0.046 0.583 0.960 1.000 0.8 500 0.074 0.204 0.822 1.000 0.039 0.264 0.643 0.944 1000 0.074 0.435 0.987 1.000 0.044 0.403 0.827 0.989 2000 0.072 0.814 1.000 1.000 0.048 0.621 0.948 0.999 0.9 500 0.095 0.190 0.849 1.000 0.045 0.391 0.720 0.939 1000 0.101 0.370 0.991 1.000 0.045 0.550 0.858 0.976 2000 0.101 0.847 1.000 1.000 0.043 0.694 0.931 0.997 τ = 0 . 5 0.6 500 0.384 0.958 1.000 0.372 0.853 0.998 1000 0.728 1.000 1.000 0.627 0.975 1.000 2000 0.958 1.000 1.000 0.856 0.998 1.000 0.7 500 0.392 0.962 1.000 0.395 0.858 0.995 1000 0.736 0.999 1.000 0.629 0.974 1.000 2000 0.964 1.000 1.000 0.869 0.997 1.000 0.8 500 0.369 0.969 1.000 0.462 0.860 0.993 1000 0.734 1.000 1.000 0.670 0.963 0.999 2000 0.966 1.000 1.000 0.851 0.996 1.000 0.9 500 0.311 0.977 1.000 0.583 0.875 0.980 1000 0.739 0.998 1.000 0.736 0.946 0.996 2000 0.979 1.000 1.000 0.860 0.987 1.000