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Change-point detection for the link function in a single-index model

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  • Yang, Qing
  • Zhang, Yi

Abstract

This article investigates the test size and power of a weighted-residual-based cumulative-sum (CUSUM) statistic for detecting the change of the link function in a single-index model. The asymptotic distributions of the CUSUM statistic are derived under the null hypothesis (when there is no change point) and the local alternative hypothesis (when there is a change with the size of order root n), and the importance of the weight function is analyzed further. Numerical performance of the test statistic is investigated using simulated data and is well satisfactory. In particular, as an extension, a single-index heterogeneous autoregressive model is built for the analysis of the realized volatilities of the S&P 500 index from 2016 to 2017, and 5 change points are detected by the proposed detection method.

Suggested Citation

  • Yang, Qing & Zhang, Yi, 2022. "Change-point detection for the link function in a single-index model," Statistics & Probability Letters, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:stapro:v:186:y:2022:i:c:s0167715222000608
    DOI: 10.1016/j.spl.2022.109468
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    References listed on IDEAS

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