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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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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Su, Liangjun & Chen, Qihui, 2013. "Testing Homogeneity In Panel Data Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1079-1135, December.
    3. Maria Mohr & Leonie Selk, 2020. "Estimating change points in nonparametric time series regression models," Statistical Papers, Springer, vol. 61(4), pages 1437-1463, August.
    4. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    5. Qing Yang & Yu-Ning Li & Yi Zhang, 2020. "Change point detection for nonparametric regression under strongly mixing process," Statistical Papers, Springer, vol. 61(4), pages 1465-1506, August.
    6. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    7. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    8. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    9. Su, Liangjun & Wang, Xia, 2020. "Testing For Structural Changes In Factor Models Via A Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1127-1158, December.
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