TIME: 4:00pm
PLACE: Cathedral of Learning
SPEAKER: Robert Krafty
ABSTRACT: Existing methods in non-statinary time series classification assume time series from different units within a population are generated by the same underlying stochastic process characterized by a time-varying second order spectrum, and both the between-time-series variability and the within-time-series variability are results of the same underlying stochastic process. This is usually not true in real applications and can lead to misclassification. In this talk, we propose a model for a family of time series by imposing a hierarchical structure on their log-spectra. This model assumes that while a family of time series share some similarity characterized by the population-average spectrum, each time series has its own characteristics modeled by the unit-specific deviation in terms of its log-spectrum. We then propose nonparametric methods to estimate the population-average log-spectrum and the between-unit variance function. We develop a quadratic rule for discriminating between different populations based on the estimated mean log-spectra and the variance functions. A simulation study is presented to empirically demonstrate the benefits of accounting for the between-time-series variability and the proposed procedure is used to discriminate pre-seizure EEG time series from non-seizure baseline data.
KEY WORDS: Discriminant Analysis; Locally Stationary Time Series; Penalized Likelihood; Smoothing Spline; Spectral Analysis.