A comparison of the finite sample performance of the testing procedures shows that: All in all, our simulation results give rise to choosing the self-normalized Wilcoxon test over the other testing procedures when testing for a change in the mean. We will now investigate the finite sample performance of the CUSUM and Wilcoxon change- point tests for detecting changes in the variance of LMSV time series { X$_{j}$, j ≥ 1 } , i.e. we choose ψ ( x ) = x 2 for the test statistics described in Section 3 and Section 5. For this purpose, we simulate observations X$_{1}$, . . . , X$_{n}$ which satisfy (16) with { ε$_{j}$, j ≥ 1 } that follow a two-sided Pareto distribution, centered to mean zero, i.e. ε$_{j}$ = ˜ ε$_{j}$ − E ˜ ε$_{0}$ , where { ˜ ε$_{j}$, j ≥ 1 } are Pareto distributed with parameter α > 4. Since Var( ε$_{1}$ ) = Var(˜ ε$_{1}$ ) = α α − 2 1 ( α − 1) 2 , we have Since E( ψ ( X$_{1}$ ) | F $_{0}$) = 0, the limits of the CUSUM statistics depend on the Hurst parameter H . 6.2 Change in the variance • In most cases the size of the CUSUM test does not deviate much from the level of significance whereas the Wilcoxon change-point test suffers from size distortions: the empirical size of the Wilcoxon test is considerably higher than the level of significance. • The self-normalized change-point tests have considerably better size properties than the non-self-normalized tests. The self-normalized Wilcoxon test is rather conserva- tive while the rejection rates of the self-normalized CUSUM test are close to the level of significance. • The power of the self-normalized Wilcoxon test is higher than the power of the self- normalized CUSUM test for almost every combination of parameters. Var( X$_{1}$ ) = E(exp(2 Y$_{1}$ )) Var( ε$_{1}$ ) = exp(2) α α − 2 1 ( α − 1) $_{2}$. 27