Discrimination of Nonstationary Time Series using SLEX Model

Abstract

Statistical discrimination for nonstationary random processes is important in many applications. In this talk, I will introduce a discriminant scheme that can extract local features of the time series, was consistent, and computationally efficient. This discriminant scheme is based on the SLEX (Smooth Localized Complex Exponential) library. The SLEX library forms a collection of Fourier-type basese that are simultaneously orthogonal and localized in both time and frequency domains. Thus, the SLEX library has the ability to extract local spectral features of the time series. The first step in this discriminant scheme, which is the feature extraction step based on Saito (1994), is to find a basis from the SLEX library that can best illuminate the difference between two or more classes of time series. In the next step, a discriminant criterion that is related to the Kullback-Leibler divergence between the SLEX spectra of the different classes is proposed. The optimal property of this method, simulations and a real data analysis will also be shown in this talk.