Yale University
Department of Statistics

Monday February 26, 1996
Sudeshna Adak
Department of Statistics
Stanford University

Title: Time-dependent Spectral Analysis of Nonstationary Time Series

Modeling of nonstationary stochastic time series has found wide applications in speech processing, biomedical signal processing, seismology and failure detection. The problem of defining a time-dependent spectrum for a general class of nonstationary processes is discussed in the context of problems in geophysics and speech processing. An appropriate definition of time-dependent spectra is proposed for a class of nonstationary processes that are locally stationary. A tree-based segmentation algorithm of estimating the time-dependent spectrum is proposed for this class of locally stationary processes. A cross-validation procedure is suggested for an optimal bias-variance tradeoff in the procedure. This method of time-frequency analysis is compared and contrasted with wavelets, matching pursuit, and Priestley's evolutionary spectra. Different examples of locally stationary processes are considered to demonstrate the algorithm's excellent ability to adapt to the rate at which the spectrum is changing. Applications of this method to signals arising from speech recognition, earthquakes, and electrocardiograms will be considered together with their scientific implications.

Seminar to be held in Room 107, 24 Hillhouse at 11:30 pm