Under the LMSV model, the limit of the test statistic can therefore be derived by the same argument that proves Theorem 1 in Betken (2016b). As a result, T$_{n}$ ( τ$_{1}$, τ$_{2}$ ) converges in distribution to T ( m, τ$_{1}$, τ$_{2}$ ), i.e. the self-normalized Wilcoxon test statistic and the self- normalized CUSUM test statistic converge to the same limit. For all simulations we make the following specifications: where 6 Simulations X$_{j}$ = σ ( Y$_{j}$ ) ε$_{j}$, j ≥ 1 , (16) • { ε$_{j}$, j ≥ 1 } is an i.i.d. sequence; • { Y$_{j}$, j ≥ 1 } is a fractional Gaussian noise sequence generated by the function fgnSim ( fArma package in R ) with the Hurst parameter H (note that H and the memory parameter D are linked by H = 1 − D/ 2); • σ ( y ) = exp( y ). In the following, we give an overview over the main simulation results for the three testing situations described in Section 4. For all scenarios, we computed the rejection rates of the different tests under the hypothesis and different change point alternatives. We investigate the finite sample performance of the CUSUM and Wilcoxon change-point tests for detecting changes in the mean of LMSV time series { X$_{j}$, j ≥ 1 } , i.e. we choose ψ ( x ) = x for the test statistics described in Section 3 and Section 5. We consider two different scenarios: 6.1 Change in the mean 22