Bootstrap Testing for Changes in Persistence with Heavy-Tailed Innovations

This article considers the problem of detection for changes in persistence with heavy-tailed innovations. We adopt a ratio type test and derive its null asymptotic distribution which is dependent on the stable index. Then a residual-based bootstrap is proposed when the stable index is unknown. Our procedure requires drawing bootstrap samples of size m < T, T being the size of original sample. We establish the convergence in probability of the bootstrap distribution function assuming that m → ∞ and m/T → 0. A Monte Carlo study has shown that the bootstrap improve the finite sample size and power compared to the asymptotic test, especially for small stable index.