Preprint
Spectral Change Point Estimation for High Dimensional Time Series by Sparse Tensor Decomposition
ArXiv.org
05/17/2023
DOI: 10.48550/arxiv.2305.10656
Abstract
We study the problem of change point (CP) detection with high dimensional
time series, within the framework of frequency domain. The overarching goal is
to locate all change points and for each change point, delineate which series
are activated by the change, over which set of frequencies. The working
assumption is that only a few series are activated per change and frequency. We
solve the problem by computing a CUSUM tensor based on spectra estimated from
blocks of the observed time series. A frequency-specific projection approach is
applied to the CUSUM tensor for dimension reduction. The projection direction
is estimated by a proposed sparse tensor decomposition algorithm. Finally, the
projected CUSUM vectors across frequencies are aggregated by a sparsified wild
binary segmentation for change point detection. We provide theoretical
guarantees on the number of estimated change points and the convergence rate of
their locations. We derive error bounds for the estimated projection direction
for identifying the frequency-specific series that are activated in a change.
We provide data-driven rules for the choice of parameters. We illustrate the
efficacy of the proposed method by simulation and a stock returns application.
Details
- Title: Subtitle
- Spectral Change Point Estimation for High Dimensional Time Series by Sparse Tensor Decomposition
- Creators
- Xinyu ZhangKung-Sik Chan
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2305.10656
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 05/17/2023
- Academic Unit
- Statistics and Actuarial Science; Radiology
- Record Identifier
- 9984413078202771
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