Detecting abrupt changes in a piecewise locally stationary time series

Authors:
Michael Last;Robert Shumway
Affiliations:
National Institute of Statistical Sciences, 19 T.W. Alexander Dr., Research Triangle Park, NC 27709, USA;Department of Statistics, University of California at Davis, Davis, CA 95616, USA
Venue:
Journal of Multivariate Analysis
Year:
2008

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Abstract

Non-stationary time series arise in many settings, such as seismology, speech-processing, and finance. In many of these settings we are interested in points where a model of local stationarity is violated. We consider the problem of how to detect these change-points, which we identify by finding sharp changes in the time-varying power spectrum. Several different methods are considered, and we find that the symmetrized Kullback-Leibler information discrimination performs best in simulation studies. We derive asymptotic normality of our test statistic, and consistency of estimated change-point locations. We then demonstrate the technique on the problem of detecting arrival phases in earthquakes.