Statistics and Its Interface

Volume 9 (2016)

Number 1

Sieve bootstrap monitoring persistence change in long memory process

Pages: 37 – 45



Zhanshou Chen (Department of Mathematics, Qinghai Normal University, Xining, Qinghai, China)

Zheng Tian (Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, China)

Yuhong Xing (Department of Mathematics, Qinghai Normal University, Xining, Qinghai, China)


This paper adopts a moving ratio statistic to monitor persistence change in long memory process. The limiting distribution of monitoring statistic under the stationary long memory null hypothesis is derived. We show that the proposed monitoring scheme is consistent for stationary to nonstationary change. In particular, a sieve bootstrap approximation method is proposed. The sieve bootstrap method is used to determine the critical values for the null distribution of monitoring statistic which depends on unknown long memory parameter. The empirical size, power and average run length of the proposed monitoring procedure are evaluated in a simulation study. Simulations indicate that the new monitoring procedure performs well in finite samples. Finally, we illustrate our monitoring procedure using a set of foreign exchange rate data.


change in persistence, long memory process, sieve bootstrap, monitoring

2010 Mathematics Subject Classification

Primary 60G22, 62F40. Secondary 62L10.

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Published 22 October 2015