Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Change points detection for nonstationary multivariate time series

  • Yeonjoo Park (Department of Management Science and Statistics, University of Texas at San Antonio) ;
  • Hyeongjun Im (Department of Applied Statistics, Chung-Ang University) ;
  • Yaeji Lim (Department of Applied Statistics, Chung-Ang University)
  • Received : 2022.11.08
  • Accepted : 2022.12.01
  • Published : 2023.07.31
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Abstract

In this paper, we develop the two-step procedure that detects and estimates the position of structural changes for multivariate nonstationary time series, either on mean parameters or second-order structures. We first investigate the presence of mean structural change by monitoring data through the aggregated cumulative sum (CUSUM) type statistic, a sequential procedure identifying the likely position of the change point on its trend. If no mean change point is detected, the proposed method proceeds to scan the second-order structural change by modeling the multivariate nonstationary time series with a multivariate locally stationary Wavelet process, allowing the time-localized auto-correlation and cross-dependence. Under this framework, the estimated dynamic spectral matrices derived from the local wavelet periodogram capture the time-evolving scale-specific auto- and cross-dependence features of data. We then monitor the change point from the lower-dimensional approximated space of the spectral matrices over time by applying the dynamic principal component analysis. Different from existing methods requiring prior information on the type of changes between mean and covariance structures as an input for the implementation, the proposed algorithm provides the output indicating the type of change and the estimated location of its occurrence. The performance of the proposed method is demonstrated in simulations and the analysis of two real finance datasets.

Keywords

Acknowledgement

This research was supported by the Chung-Ang University Graduate Research Scholarship in 2021, the National Research Foundation of Korea (NRF) funded by the Korea government (2022R1F1A1074134), and Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry and Energy (MOTIE) of the Republic of Korea (No.20199710100060).

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