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Journal of the American Statistical Association Volume 96, 2001 - Issue 454
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Primary Article

Automatic Statistical Analysis of Bivariate Nonstationary Time Series

Hernando C Ombao Hernando C. Ombao is Assistant Professor, Departments of Statistics and Psychiatry, University of Pittsburgh, Pittsburgh, PA 15260 . Jonathan A. Raz, who passed away on February 23, 2000, was Associate Professor, Division of Biostatistics, University of Pennsylvania, Philadelphia, PA 19104. Rainer von Sachs is Professor, Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium . Beth A. Malow is Assistant Professor, Department of Neurology, University of Michigan, Ann Arbor, MI 48109 . H. Ombao was supported by NIH grants MH51310, MH62298, and MH30195. J. Raz was supported, in part, by NIH R29 MH51310. R. von Sachs was supported by grant PARC 98/03-217 from the Belgian government. B. Malow was supported by NINDS grant 1 K08 NS01840. The authors thank the Associate Editor and the referees for making helpful comments and suggestions.
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Jonathan A Raz Hernando C. Ombao is Assistant Professor, Departments of Statistics and Psychiatry, University of Pittsburgh, Pittsburgh, PA 15260 . Jonathan A. Raz, who passed away on February 23, 2000, was Associate Professor, Division of Biostatistics, University of Pennsylvania, Philadelphia, PA 19104. Rainer von Sachs is Professor, Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium . Beth A. Malow is Assistant Professor, Department of Neurology, University of Michigan, Ann Arbor, MI 48109 . H. Ombao was supported by NIH grants MH51310, MH62298, and MH30195. J. Raz was supported, in part, by NIH R29 MH51310. R. von Sachs was supported by grant PARC 98/03-217 from the Belgian government. B. Malow was supported by NINDS grant 1 K08 NS01840. The authors thank the Associate Editor and the referees for making helpful comments and suggestions.
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Rainer von Sachs Hernando C. Ombao is Assistant Professor, Departments of Statistics and Psychiatry, University of Pittsburgh, Pittsburgh, PA 15260 . Jonathan A. Raz, who passed away on February 23, 2000, was Associate Professor, Division of Biostatistics, University of Pennsylvania, Philadelphia, PA 19104. Rainer von Sachs is Professor, Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium . Beth A. Malow is Assistant Professor, Department of Neurology, University of Michigan, Ann Arbor, MI 48109 . H. Ombao was supported by NIH grants MH51310, MH62298, and MH30195. J. Raz was supported, in part, by NIH R29 MH51310. R. von Sachs was supported by grant PARC 98/03-217 from the Belgian government. B. Malow was supported by NINDS grant 1 K08 NS01840. The authors thank the Associate Editor and the referees for making helpful comments and suggestions.
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Beth A Malow Hernando C. Ombao is Assistant Professor, Departments of Statistics and Psychiatry, University of Pittsburgh, Pittsburgh, PA 15260 . Jonathan A. Raz, who passed away on February 23, 2000, was Associate Professor, Division of Biostatistics, University of Pennsylvania, Philadelphia, PA 19104. Rainer von Sachs is Professor, Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium . Beth A. Malow is Assistant Professor, Department of Neurology, University of Michigan, Ann Arbor, MI 48109 . H. Ombao was supported by NIH grants MH51310, MH62298, and MH30195. J. Raz was supported, in part, by NIH R29 MH51310. R. von Sachs was supported by grant PARC 98/03-217 from the Belgian government. B. Malow was supported by NINDS grant 1 K08 NS01840. The authors thank the Associate Editor and the referees for making helpful comments and suggestions.
Pages 543-560 | Published online: 31 Dec 2011
 
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Abstract

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.

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