Discrimination of Locally Stationary Time Series Based on the Excess Mass Functional

Abstract

Discrimination of time series is an important practical problem with applications in various scientific fields. We propose and study a novel approach to this problem. Our approach is applicable to cases where time series in different categories have a different “shape.” Although based on the idea of feature extraction, our method is not distance-based, and as such does not require aligning the time series. Instead, features are measured for each time series, and discrimination is based on these individual measures. An AR process with a time-varying variance is used as an underlying model. Our method then uses shape measures or, better, measures of concentration of the variance function, as a criterion for discrimination. It is this concentration aspect or shape aspect that makes the approach intuitively appealing. We provide some mathematical justification for our proposed methodology, as well as a simulation study and an application to the problem of discriminating earthquakes and explosions.