The SLEX Analysis of Multivariate Non-Stationary Time Series

• Activity Number: 301
• Type: Topic Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Hernando Ombao*+
• Affiliation(s): University of Pittsburgh
• Keywords: Non-Stationary Time Series ; Time-dependent spectral analysis ; Fourier transform ; SLEX transform ; periodogram smoothing

Abstract

In this article, we discuss an analysis of multivariate non-stationary time series using SLEX (Smooth Localized Complex EXponentials) transform, which form a rich library of orthogonal bases. In our approach, we build a family of SLEX models, each of which uses a unique SLEX basis as stochastic building blocks. The SLEX basis are a localized version of the Fourier basis and, hence, they are ideal at representing processes whose spectrum evolves over time. The SLEX analysis for non-stationary time series is in the spirit of traditional Fourier analysis for stationary time series. The SLEX method, analogous to the Fourier method, smooths the SLEX periodogram matrix across frequency to obtain a consistent estimator of the time-dependent spectrum. In this talk, we present the steps in the complete SLEX analysis, namely: i.) build the family of SLEX models; ii.) select the best model using an objective criterion; and iii.) estimate the time-dependent spectral density matrix. Moreover, we will introduce a frequency domain principal components analysis that is based on the SLEX. We apply the SLEX analysis to a brain wave's dataset recorded during an epileptic seizure.