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Detecting abrupt changes in a piecewise locally stationary time series

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  • Last, Michael
  • Shumway, Robert

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.

Suggested Citation

  • Last, Michael & Shumway, Robert, 2008. "Detecting abrupt changes in a piecewise locally stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 191-214, February.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:2:p:191-214
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    References listed on IDEAS

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    1. Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
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    4. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    5. D. S. Coates & P. J. Diggle, 1986. "Tests For Comparing Two Estimated Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 7-20, January.
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    4. Jin, Hao & Zhang, Jinsuo, 2010. "Subsampling tests for variance changes in the presence of autoregressive parameter shifts," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2255-2265, November.

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