IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v71y2019i5d10.1007_s10463-018-0679-4.html
   My bibliography  Save this article

Modified residual CUSUM test for location-scale time series models with heteroscedasticity

Author

Listed:
  • Haejune Oh

    (Seoul National University)

  • Sangyeol Lee

    (Seoul National University)

Abstract

This study considers the residual-based CUSUM test for location-scale time series models with heteroscedasticity. The estimates- and score vector-based CUSUM tests are widely used for detecting abrupt changes in time series models. However, their performance is often unsatisfactory with severe size distortions when the underlying model is complicated and the sample size is small. To circumvent this defect, the residual-based CUSUM test is suggested as an alternative. However, this test can only detect scale parameter changes and suffers severe power loss against location parameter changes. To remedy this, we introduce a modified residual-based CUSUM test and demonstrate its validity for both location and scale parameter changes. We conduct a simulation study and data analysis for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0679-4
    DOI: 10.1007/s10463-018-0679-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-018-0679-4
    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/s10463-018-0679-4?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. 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.
    2. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    3. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1236-1278, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. de Pooter, M.D. & van Dijk, D.J.C., 2004. "Testing for changes in volatility in heteroskedastic time series - a further examination," Econometric Institute Research Papers EI 2004-38, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Lee, Sangyeol & Song, Junmo, 2008. "Test for parameter change in ARMA models with GARCH innovations," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1990-1998, September.
    10. Jürgen Franke & Claudia Kirch & Joseph Tadjuidje Kamgaing, 2012. "Changepoints in times series of counts," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(5), pages 757-770, September.
    11. Claudia Kirch & Joseph Tadjuidje Kamgaing, 2012. "Testing for parameter stability in nonlinear autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 365-385, May.
    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. Gabriela Ciuperca, 2022. "Real-time detection of a change-point in a linear expectile model," Statistical Papers, Springer, vol. 63(4), pages 1323-1367, August.

    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. Mamadou Lamine Diop & William Kengne, 2023. "A general procedure for change-point detection in multivariate time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 1-33, March.
    3. Song, Junmo & Kang, Jiwon, 2018. "Parameter change tests for ARMA–GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 41-56.
    4. 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.
    5. 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.
    6. Youngmi Lee & Sangyeol Lee & Dag Tjøstheim, 2018. "Asymptotic normality and parameter change test for bivariate Poisson INGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 52-69, March.
    7. Lee, Sangyeol & Kim, Dongwon & Kim, Byungsoo, 2023. "Modeling and inference for multivariate time series of counts based on the INGARCH scheme," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    8. Mamadou Lamine Diop & William Kengne, 2017. "Testing Parameter Change in General Integer-Valued Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 880-894, November.
    9. repec:cte:wsrepe:ws131718 is not listed on IDEAS
    10. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    11. 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.
    12. Lee, Sangyeol & Oh, Haejune, 2015. "Entropy test and residual empirical process for autoregressive conditional duration models," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 1-12.
    13. 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.
    14. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    15. Maria Mohr & Natalie Neumeyer, 2021. "Nonparametric volatility change detection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 529-548, June.
    16. Cho, Haeran & Korkas, Karolos K., 2022. "High-dimensional GARCH process segmentation with an application to Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 23(C), pages 187-203.
    17. 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.
    18. Lee, Sangyeol, 2006. "The Bickel-Rosenblatt test for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1494-1502, August.
    19. 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.
    20. 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.
    21. 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.

    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:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0679-4. 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.