Discrimination and Classification of Nonstationary Time Series Using the SLEX Model.

Statistical discrimination for nonstationary random processes is important in many applications. Our goal was to develop a discriminant scheme that can extract local features of the time series, is consistent, and is computationally efficient. Here, we purpose a discriminant scheme based on the SLEX (smooth localized complex exponential) library. The SLEX library forms a collection of Fourier-type bases 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 our procedure, which is the feature extraction step based on work by Saito, 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, we construct a discriminant criterion that is related to the Kullback-Leibler divergence between the SLEX spectra of the different classes. The discrimination criterion is based on estimates of the SLEX spectra that are computed using the SLEX basis selected in the feature extraction step. We show that the discrimination method is consistent and demonstrate via finite sample simulation studies that our proposed method performs well. Finally, we apply our method to a seismic waves dataset with the primary purpose of classifying the origin of an unknown seismic recording as either an earthquake or an explosion. [ABSTRACT FROM AUTHOR]