Abstract #300675

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JSM 2003 Abstract #300675
Activity Number: 393
Type: Invited
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #300675
Title: The SLEX Analysis of Multivariate Nonstationary Time Series
Author(s): Hernando Ombao*+ and Rainer von Sachs and Wensheng Guo
Companies: University of Illinois and Université Catholique de Louvain and University of Pennsylvania
Address: Department of Statistics, Champaign, IL, 61820,
Keywords: nonstationary time series ; SLEX transform ; spectral analysis ; principal components analysis
Abstract:

Many time series are non-tationary in nature. As examples, brain waves and seismic waves have time-varying amplitudes and oscillate at frequencies that vary over time. We use the SLEX transform (Smooth Localized Complex Exponentials) which forms a collection of orthogonal localized Fourier bases. We will present the sequential steps in the SLEX analysis of multivariate nonstationary time series. First, we build a family of SLEX models, each of which has a spectral representation in terms of a unique SLEX basis. Second, we select the best model using a criterion that is based on the Kullback-Leibler divergence measure. The selected model gives us a time-frequency representation of the multivariate time series. Based on the best spectral representation, we obtain time-varying spectral, coherence and lag estimates by smoothing the SLEX periodograms and cross-periodograms across frequency. Finally, to reduce dimensionality in the data, we perform a time-dependent principal-components analysis on the SLEX coefficients. We illustrate the SLEX method using a brain waves dataset recorded during an epileptic seizure.

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