Estimation of the evolutionary spectra with application to stationarity test

Yu Xiang, Jie Ding, Vahid Tarokh

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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
Issue number5
StatePublished - Mar 1 2019

Bibliographical note

Funding Information:
Manuscript received February 24, 2018; revised September 26, 2018 and October 29, 2018; accepted November 26, 2018. Date of publication January 1, 2019; date of current version January 16, 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. D. Robert Iskander. This work was supported by Defense Advanced Research Projects Agency (DARPA) under Grants W911NF-14-1-0508, W911NF-16-1-0561, and N66001-15-C-4028. (Corresponding author: Yu Xiang.) Y. Xiang is with the Electrical and Computer Engineering Department, University of Utah, Salt Lake City, UT 84112 USA (e-mail:,

Publisher Copyright:
© 2018 IEEE.


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


Dive into the research topics of 'Estimation of the evolutionary spectra with application to stationarity test'. Together they form a unique fingerprint.

Cite this