Bootstrap testing multiple changes in persistence for a heavy-tailed sequence

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• 作者：Zhanshou Chen^a ; ^b ; ^{chenzhanshou@126.com} ; Zi Jin^c ; Zheng Tian^b ; ^d ; Peiyan Qi^b
• 关键词：Multiple changes in persistence ; Moving ratio test ; Bootstrap ; Heavy tailed
• 刊名：Computational Statistics and Data Analysis
• 出版年：2012
• 期刊代码：19_01679473
• 类别：cp
• 出版时间：July, 2012
• 卷：56
• 期：7
• 页码：2303-2316
• 文件大小：267 K

摘要

This paper tests the null hypothesis of stationarity against the alternative of changes in persistence for sequences in the domain of attraction of a stable law. The proposed moving ratio test is valid for multiple changes in persistence while the previous residual based ratio tests are designed for processes displaying only a single change. We show that the new test is consistent whether the process changes from to or vice versa. And it is easy to identify the direction of detected change points. In particular, a bootstrap approximation method is proposed to determine the critical values for the null distribution of the test statistic containing unknown tail index. We also propose a two step approach to estimate the change points. Numerical evidence suggests that our test performs well in finite samples. In addition, we show that our test is still powerful for changes between short and long memory, and displays no tendency to spuriously over-reject null in favor of a persistence change if the process is actually throughout. Finally, we illustrate our test using the US聽inflation rate data and a set of high frequency stock closing price data.