SLEX analysis of multivariate nonstationary time series

Hernando Ombao*, Rainer Von Sachs, Wensheng Guo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


We develop a procedure for analyzing multivariate nonstationary time series using the SLEX library (smooth localized complex exponentials), which is a collection of bases, each basis consisting of waveforms that are orthogonal and time-localized versions of the Fourier complex exponentials. Under the SLEX framework, we build a family of multivariate models that can explicitly characterize the time-varying spectral and coherence properties. Every model has a spectral representation in terms of a unique SLEX basis. Before selecting a model, we first decompose the multivariate time series into nonstationary components with uncorrelated (nonredundant) spectral information. The best SLEX model is selected using the penalized log energy criterion, which we derive in this article to be the Kullback-Leibler distance between a model and the SLEX principal components of the multivariate time series. The model selection criterion takes into account all of the pairwise cross-correlation simultaneously in the multivariate time series. The proposed SLEX analysis gives results that are easy to interpret, because it is an automatic time-dependent generalization of the classical Fourier analysis of stationary time series. Moreover, the SLEX method uses computationally efficient algorithms and hence is able to provide a systematic framework for extracting spectral features from a massive dataset. We illustrate the SLEX analysis with an application to a multichannel brain wave dataset recorded during an epileptic seizure.

Original languageEnglish (US)
Pages (from-to)519-531
Number of pages13
Issue number470
StatePublished - Jun 2005
Externally publishedYes


  • Multivariate nonstationary time series
  • SLEX model
  • SLEX principal components
  • SLEX transform
  • Time-frequency analysis
  • Time-varying spectral matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'SLEX analysis of multivariate nonstationary time series'. Together they form a unique fingerprint.

Cite this