Detecting abrupt changes in a piecewise locally stationary time series

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.