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Empirical Frequency Band Analysis of Nonstationary Time Series

Author

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  • Scott A. Bruce
  • Cheng Yong Tang
  • Martica H. Hall
  • Robert T. Krafty

Abstract

The time-varying power spectrum of a time series process is a bivariate function that quantifies the magnitude of oscillations at different frequencies and times. To obtain low-dimensional, parsimonious measures from this functional parameter, applied researchers consider collapsed measures of power within local bands that partition the frequency space. Frequency bands commonly used in the scientific literature were historically derived, but they are not guaranteed to be optimal or justified for adequately summarizing information from a given time series process under current study. There is a dearth of methods for empirically constructing statistically optimal bands for a given signal. The goal of this article is to provide a standardized, unifying approach for deriving and analyzing customized frequency bands. A consistent, frequency-domain, iterative cumulative sum based scanning procedure is formulated to identify frequency bands that best preserve nonstationary information. A formal hypothesis testing procedure is also developed to test which, if any, frequency bands remain stationary. The proposed method is used to analyze heart rate variability of a patient during sleep and uncovers a refined partition of frequency bands that best summarize the time-varying power spectrum. Supplementary materials for this article are available online.

Suggested Citation

  • Scott A. Bruce & Cheng Yong Tang & Martica H. Hall & Robert T. Krafty, 2020. "Empirical Frequency Band Analysis of Nonstationary Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1933-1945, December.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:532:p:1933-1945
    DOI: 10.1080/01621459.2019.1671199
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    Cited by:

    1. Granados-Garcia, Guilllermo & Fiecas, Mark & Babak, Shahbaba & Fortin, Norbert J. & Ombao, Hernando, 2022. "Brain waves analysis via a non-parametric Bayesian mixture of autoregressive kernels," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    2. Marie Tuft & Martica H. Hall & Robert T. Krafty, 2023. "Spectra in low‐rank localized layers (SpeLLL) for interpretable time–frequency analysis," Biometrics, The International Biometric Society, vol. 79(1), pages 304-318, March.

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