Block Bootstrap Tests for Persistence Change in Heavy-Tailed Dependent Sequence
In this paper,we discuss the problem of persistence change test for heavy-tailed dependent sequences where the tail index κ ∈(0,2).The modified test statistics are constructed based on the Dickey-Fuller(DF)ratio type statistics,and its asymp-totic distribution under the null hypothesis is proven to be a functional of a stable process.Under the alternative hypothesis,the test statistics are consistent and can correctly identify the persistence direction of change.At the same time,the consis-tency of the change point location estimation is also given.When the sequence is a stationary process,the constructed test statistics will not generate spurious rejection.Since the asymptotic distribution of the statistic under the null hypothesis contains the unknown parameter κ,the critical value of the statistic is determined by using the Block Bootstrap sampling method to avoid the estimation of the tail index κ.The Monte Carlo numerical simulation results fully demonstrate the robustness of the proposed test statistics.Finally,the feasibility and effectiveness of the proposed method are illustrated by a set of stock data.
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