IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v27y2018i3d10.1007_s10260-017-0408-9.html
   My bibliography  Save this article

On score vector- and residual-based CUSUM tests in ARMA–GARCH models

Author

Listed:
  • Haejune Oh

    (Seoul National University)

  • Sangyeol Lee

    (Seoul National University)

Abstract

In this study, we consider the problem of testing for a parameter change in ARMA–GARCH models. We suggest two types of cumulative sum (CUSUM) tests, namely, score vector- and residual-based CUSUM tests. It is shown that under regularity conditions, their limiting null distributions are the sup of Brownian bridges. A simulation study and real data analysis are conducted for illustration.

Suggested Citation

  • Haejune Oh & Sangyeol Lee, 2018. "On score vector- and residual-based CUSUM tests in ARMA–GARCH models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 385-406, August.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:3:d:10.1007_s10260-017-0408-9
    DOI: 10.1007/s10260-017-0408-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-017-0408-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-017-0408-9?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. Sangyeol Lee & Siyun Park, 2001. "The Cusum of Squares Test for Scale Changes in Infinite Order Moving Average Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 625-644, December.
    2. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    3. Koichi Maekawa & Sangyeol & Lee, 2004. "The Cusum Test for Parameter Change in Regression with ARCH Errors," Econometric Society 2004 Far Eastern Meetings 606, Econometric Society.
    4. Berkes, Istvan & Horváth, Lajos & Kokoszka, Piotr, 2004. "Testing for parameter constancy in GARCH(p,q) models," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 263-273, December.
    5. Berkes, István & Gombay, Edit & Horváth, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1140-1167, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Minyoung Jo & Sangyeol Lee, 2021. "On CUSUM test for dynamic panel models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 515-542, June.

    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. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.
    2. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(3), pages 809-822, June.
    3. Lee, Sangyeol & Park, Siyun, 2009. "The monitoring test for the stability of regression models with nonstationary regressors," Economics Letters, Elsevier, vol. 105(3), pages 250-252, December.
    4. Ai Deng & Pierre Perron, 2005. "The Limit Distribution of the CUSUM of Square Test Under Genreal MIxing Conditions," Boston University - Department of Economics - Working Papers Series WP2005-046, Boston University - Department of Economics.
    5. Song, Junmo & Kang, Jiwon, 2018. "Parameter change tests for ARMA–GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 41-56.
    6. Haejune Oh & Sangyeol Lee, 2019. "Modified residual CUSUM test for location-scale time series models with heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1059-1091, October.
    7. Minyoung Jo & Sangyeol Lee, 2021. "On CUSUM test for dynamic panel models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 515-542, June.
    8. Okyoung Na & Jiyeon Lee & Sangyeol Lee, 2013. "Change point detection in SCOMDY models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 215-238, July.
    9. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    10. Koichi Maekawa & Sangyeol & Lee, 2004. "The Cusum Test for Parameter Change in Regression with ARCH Errors," Econometric Society 2004 Far Eastern Meetings 606, Econometric Society.
    11. Philip Preuss & Ruprecht Puchstein & Holger Dette, 2015. "Detection of Multiple Structural Breaks in Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 654-668, June.
    12. Chen, Zhanshou & Tian, Zheng, 2010. "Modified procedures for change point monitoring in linear models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 62-75.
    13. Lee, Sangyeol, 2006. "The Bickel-Rosenblatt test for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1494-1502, August.
    14. Habibi Reza, 2011. "A note on approximating distribution functions of cusum and cusumsq tests," Monte Carlo Methods and Applications, De Gruyter, vol. 17(1), pages 1-10, January.
    15. Josephine Njeri Ngure & Anthony Gichuhi Waititu, 2021. "Consistency of an Estimator for Change Point in Volatility of Financial Returns," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 13(1), pages 1-56, February.
    16. Manh Cuong Dong & Cathy W. S. Chen & Sangyoel Lee & Songsak Sriboonchitta, 2019. "How Strong is the Relationship Among Gold and USD Exchange Rates? Analytics Based on Structural Change Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 343-366, January.
    17. Okyoung Na & Youngmi Lee & Sangyeol Lee, 2011. "Monitoring parameter change in time series models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 171-199, June.
    18. Haipeng Xing & Hongsong Yuan & Sichen Zhou, 2017. "A Mixtured Localized Likelihood Method for GARCH Models with Multiple Change-points," Review of Economics & Finance, Better Advances Press, Canada, vol. 8, pages 44-60, May.
    19. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
    20. Lee, Sangyeol & Na, Okyoung, 2005. "Test for parameter change in stochastic processes based on conditional least-squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 375-393, April.

    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:spr:stmapp:v:27:y:2018:i:3:d:10.1007_s10260-017-0408-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.