Persistence Changes Test for Heavy Tail Series in the Presence of Index Breaks

Xuefeng WANG, Yuanyuan LI, Dan ZHANG


In this paper we consider the effect of persistence change test when the series exist an index change point at the moment. It is shown that under the null hypothesis that the circumstance of the series only existed an index change point, if the heavy tail index  change from large to small, the statistics is diverging at a rate of , and the larger of the  is, the faster the divergence is. If the index change from small to large, the statistics converges to the bounded constant. The numerical simulation shows that no matter how the change of  will lead to the size distortions, and the size distortions shows more serious when k1 > k2. 


Persistence change point; Heavy tail series; Ratio statistics

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