Automatic statistical analysis of bivariate nonstationary time series

Hernando Ombao*, Jonathan A. Raz, Rainer von Sachs, Beth A. Malow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

130 Scopus citations


We propose a new method for analyzing bivariate nonstationary time series. The proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span to be used to obtain the smoothed estimates of the time-varying spectra and coherence. It is based on the smooth localized complex exponential (SLEX) transform, which forms a library of orthogonal complex-valued transforms that are simultaneously localized in time and frequency. We show that the smoothed SLEX periodograms are consistent estimators, report simulation results, and apply the method to a two-channel electroencephalogram dataset recorded during an epileptic seizure.

Original languageEnglish (US)
Pages (from-to)543-560
Number of pages18
JournalJournal of the American Statistical Association
Issue number454
StatePublished - Jun 1 2001


  • Kernel smoothing
  • Nonstationary time series
  • SLEX periodogram
  • SLEX transform
  • Time-frequency analysis
  • Time-varying spectrum and coherence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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