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

  • Authors:

  • Zhanshou Chen;Zi Jin;Zheng Tian;Peiyan Qi

  • Affiliations:

  • Department of Mathematics, Qinghai Normal University, Xining, Qinghai 810008, PR China and Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China;Department of Statistics, University of British Columbia, 333-6356 Agricultural Road, Vancouver, BC V67T 1Z2, Canada;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China and National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy o ...;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2012

Quantified Score

Hi-index 0.03

Visualization

Abstract

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 I(0) to I(1) 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 I(0) null in favor of a persistence change if the process is actually I(1) throughout. Finally, we illustrate our test using the US inflation rate data and a set of high frequency stock closing price data.