Estimation of the evolutionary spectra with application to stationarity test

Yu Xiang, Jie Ding, Vahid Tarokh

Research output: Contribution to journalArticle

Abstract

In this paper, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the distinguishing feature of the evolutionary spectra is its focus on the physical meaning of frequency. The classical estimate of the evolutionary spectral density is based on a double-window technique consisting of a short-time Fourier transform and a smoothing. However, smoothing is known to suffer from the so-called bias leakage problem. By incorporating Thomson's multitaper method that was originally designed for stationary processes, we propose an improved estimate of the evolutionary spectral density, and analyze its bias/variance/resolution tradeoff. As an application of the new estimate, we further propose a non-parametric rank-based stationarity test, and provide various experimental studies.

Original languageEnglish (US)
Article number8598905
Pages (from-to)1353-1365
Number of pages13
JournalIEEE Transactions on Signal Processing
Volume67
Issue number5
DOIs
StatePublished - Mar 1 2019

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Spectral density
Fourier transforms

Keywords

  • Evolutionary spectra
  • Multitaper method
  • Non-stationary processes
  • Spectral analysis
  • Stationarity test

Cite this

Estimation of the evolutionary spectra with application to stationarity test. / Xiang, Yu; Ding, Jie; Tarokh, Vahid.

In: IEEE Transactions on Signal Processing, Vol. 67, No. 5, 8598905, 01.03.2019, p. 1353-1365.

Research output: Contribution to journalArticle

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