IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v186y2022ics0167715222000608.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222000608
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2022.109468?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Maria Mohr & Leonie Selk, 2020. "Estimating change points in nonparametric time series regression models," Statistical Papers, Springer, vol. 61(4), pages 1437-1463, August.
    3. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, 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. 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.
    6. 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.
    7. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jing Sun, 2016. "Composite quantile regression for single-index models with asymmetric errors," Computational Statistics, Springer, vol. 31(1), pages 329-351, March.
    2. Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    4. Gkillas, Konstantinos & Gupta, Rangan & Pierdzioch, Christian, 2020. "Forecasting realized oil-price volatility: The role of financial stress and asymmetric loss," Journal of International Money and Finance, Elsevier, vol. 104(C).
    5. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    6. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2020. "The contribution of intraday jumps to forecasting the density of returns," Post-Print halshs-02505861, HAL.
    7. Toshiaki Ogawa & Masato Ubukata & Toshiaki Watanabe, 2020. "Stock Return Predictability and Variance Risk Premia around the ZLB," IMES Discussion Paper Series 20-E-09, Institute for Monetary and Economic Studies, Bank of Japan.
    8. Kruse, Robinson & Leschinski, Christian & Will, Michael, 2016. "Comparing Predictive Accuracy under Long Memory - With an Application to Volatility Forecasting," Hannover Economic Papers (HEP) dp-571, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    9. Busch, Thomas & Christensen, Bent Jesper & Nielsen, Morten Ørregaard, 2011. "The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets," Journal of Econometrics, Elsevier, vol. 160(1), pages 48-57, January.
    10. Vortelinos, Dimitrios I., 2017. "Forecasting realized volatility: HAR against Principal Components Combining, neural networks and GARCH," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 824-839.
    11. repec:hum:wpaper:sfb649dp2009-028 is not listed on IDEAS
    12. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Decoupling the short- and long-term behavior of stochastic volatility," CREATES Research Papers 2017-26, Department of Economics and Business Economics, Aarhus University.
    13. Wen Cheong Chin & Min Cherng Lee, 2018. "S&P500 volatility analysis using high-frequency multipower variation volatility proxies," Empirical Economics, Springer, vol. 54(3), pages 1297-1318, May.
    14. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    15. Sévi, Benoît, 2014. "Forecasting the volatility of crude oil futures using intraday data," European Journal of Operational Research, Elsevier, vol. 235(3), pages 643-659.
    16. Cipollini, Andrea & Cascio, Iolanda Lo & Muzzioli, Silvia, 2015. "Volatility co-movements: A time-scale decomposition analysis," Journal of Empirical Finance, Elsevier, vol. 34(C), pages 34-44.
    17. Barbara Będowska-Sójka, 2018. "Is intraday data useful for forecasting VaR? The evidence from EUR/PLN exchange rate," Risk Management, Palgrave Macmillan, vol. 20(4), pages 326-346, November.
    18. Harry-Paul Vander Elst, 2015. "FloGARCH: Realizing Long Memory and Asymmetries in Returns Valitility," Working Papers ECARES ECARES 2015-12, ULB -- Universite Libre de Bruxelles.
    19. Haugom, Erik & Langeland, Henrik & Molnár, Peter & Westgaard, Sjur, 2014. "Forecasting volatility of the U.S. oil market," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 1-14.
    20. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "Estimation and Inference Procedures for Semiparametric Distribution Models with Varying Linear-Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 396-424, June.
    21. Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:186:y:2022:i:c:s0167715222000608. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.