A tail adaptive approach for change point detection

Bin Liu, Cheng Zhou and Xinsheng Zhang

Journal of Multivariate Analysis, 2019, vol. 169, issue C, 33-48

Abstract: For change point problems with Gaussian distributions, the CUSUM method is most efficient for detecting mean shifts. In contrast, it is not so efficient for heavy-tailed or contaminated data because of its sensitivity to outliers. To address this issue, Csörgő and Horváth (1988) introduced the Wilcoxon–Mann–Whitney test based on two-sample U-statistics. In practice, however, the tail structure of distributions is typically unknown. For example, Barndorff-Nielsen and Shephard (2001) showed that with higher frequency, stock returns’ tails become heavier. To our knowledge, there are no uniformly most powerful testing methods for both heavy and light-tailed distributions. To deal with this issue, we construct a new family of test statistics and combine them to adapt to different tails. As the final test statistic is complex, we design a low-cost bootstrap procedure to approximate its limiting distribution. To capture temporal data dependence, we assume that the data follow a near epoch dependent process (Borovkova et al., 2001), which includes ARMA and GARCH processes, among others. We explore the validity of our method both theoretically and through simulation. We also illustrate its use with data on the S&P 500 index.

Keywords: Change point test; Functionals of absolutely regular process; Low-cost bootstrap; Tail adaptive test; Two-sample U-statistics (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X18302100
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:169:y:2019:i:c:p:33-48

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2018.08.010

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().