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Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of interest. However, there is a dearth of data-driven methods for identifying frequency bands that optimally summarize frequency-domain information in the time series. A new method to identify partition points in the frequency space of a multivariate locally stationary time series is proposed. These partition points signify changes across frequencies in the time-varying behavior of the signal and provide frequency band summary measures that best preserve nonstationary dynamics of the observed series. An $$L_2$$-norm based discrepancy measure that finds differences in the time-varying spectral density matrix is constructed, and its asymptotic properties are derived. New nonparametric bootstrap tests are also provided to identify significant frequency partition points and to identify components and cross-components of the spectral matrix exhibiting changes over frequencies. Finite-sample performance of the proposed method is illustrated via simulations. The proposed method is used to develop optimal frequency band summary measures for characterizing time-varying behavior in resting-state electroencephalography time series, as well as identifying components and cross-components associated with each frequency partition point.
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An encoding approach for stable change point detection
Abstract Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively synthesize change-point results from all individual univariate time series into consistent and stable location estimations. We also study a weighting strategy to measure the degree of relevance for different subsampled groups. Simulation studies are conducted and shown that the proposed change-point methodology for multivariate time series has favorable performance comparing with currently available state-of-the-art nonparametric methods under various settings with different degrees of complexity. Real data analyses are finally performed on categorical, ordinal, and continuous time series taken from fields of genetics, climate, and finance.
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- Award ID(s):
- 1934568
- PAR ID:
- 10555969
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Machine Learning
- Volume:
- 113
- Issue:
- 7
- ISSN:
- 0885-6125
- Page Range / eLocation ID:
- 4133 to 4163
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1007/s10994-023-06510-x
