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A New Class of Change Point Test Statistics of Rényi Type

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  • Lajos Horváth
  • Curtis Miller
  • Gregory Rice

Abstract

A new class of change point test statistics is proposed that utilizes a weighting and trimming scheme for the cumulative sum (CUSUM) process inspired by Rényi. A thorough asymptotic analysis and simulations both demonstrate that this new class of statistics possess superior power compared to traditional change point statistics based on the CUSUM process when the change point is near the beginning or end of the sample. Generalizations of these “Rényi” statistics are also developed to test for changes in the parameters in linear and nonlinear regression models, and in generalized method of moments estimation. In these contexts, we applied the proposed statistics, as well as several others, to test for changes in the coefficients of Fama–French factor models. We observed that the Rényi statistic was the most effective in terms of retrospectively detecting change points that occur near the endpoints of the sample.

Suggested Citation

  • Lajos Horváth & Curtis Miller & Gregory Rice, 2020. "A New Class of Change Point Test Statistics of Rényi Type," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 570-579, July.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:3:p:570-579
    DOI: 10.1080/07350015.2018.1537923
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    Cited by:

    1. Lajos Horváth & Curtis Miller & Gregory Rice, 2021. "Detecting early or late changes in linear models with heteroscedastic errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 577-609, June.
    2. Fabrizio Ghezzi & Eduardo Rossi & Lorenzo Trapani, 2024. "Fast Online Changepoint Detection," Papers 2402.04433, arXiv.org.
    3. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2022. "Change point analysis of covariance functions: A weighted cumulative sum approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Ardia, David & Dufays, Arnaud & Ordás Criado, Carlos, 2023. "Linking Frequentist and Bayesian Change-Point Methods," MPRA Paper 119486, University Library of Munich, Germany.
    5. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    6. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2023. "Testing for changes in linear models using weighted residuals," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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