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Inference of breakpoints in high-dimensional time series

Author

Listed:
  • Chen, Likai
  • Wang, Weining
  • Wu, Wei Biao
Abstract
For multiple change-points detection of high-dimensional time series, we provide asymptotic theory concerning the consistency and the asymptotic distribution of the breakpoint statistics and estimated break sizes. The theory backs up a simple two- step procedure for detecting and estimating multiple change-points. The proposed two-step procedure involves the maximum of a MOSUM (moving sum) type statistics in the rst step and a CUSUM (cumulative sum) re nement step on an aggregated time series in the second step. Thus, for a xed time-point, we can capture both the biggest break across di erent coordinates and aggregating simultaneous breaks over multiple coordinates. Extending the existing high-dimensional Gaussian approximation theorem to dependent data with jumps, the theory allows us to characterize the size and power of our multiple change-point test asymptotically. Moreover, we can make inferences on the breakpoints estimates when the break sizes are small. Our theoretical setup incorporates both weak temporal and strong or weak cross-sectional dependence and is suitable for heavy-tailed innovations. A robust long-run covariance matrix estimation is proposed, which can be of independent interest. An application on detecting structural changes of the U.S. unemployment rate is considered to illustrate the usefulness of our method.

Suggested Citation

  • Chen, Likai & Wang, Weining & Wu, Wei Biao, 2020. "Inference of breakpoints in high-dimensional time series," IRTG 1792 Discussion Papers 2020-019, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    • Handle: RePEc:zbw:irtgdp:2020019
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    References listed on IDEAS

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    Cited by:

    1. Wang, Weining & Wooldridge, Jeffrey M. & Xu, Mengshan, 2020. "Improved Estimation of Dynamic Models of Conditional Means and Variances," IRTG 1792 Discussion Papers 2020-021, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Wang, Weining & Yu, Lining & Wang, Bingling, 2020. "Tail Event Driven Factor Augmented Dynamic Model," IRTG 1792 Discussion Papers 2020-022, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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    More about this item

    Keywords

    multiple change points detection; temporal and cross-sectional dependence; Gaussian approximation; inference of break locations;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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