IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v121y2018icp41-56.html
   My bibliography  Save this article

Parameter change tests for ARMA–GARCH models

Author

Listed:
  • Song, Junmo
  • Kang, Jiwon

Abstract

This paper considers the problem of testing for parameter change in ARMA–GARCH models. For this, we propose score test and residual-based cumulative sum (CUSUM) test and derive their limiting null distributions. According to our simulation study, the score test performs reasonably in testing for both ARMA and GARCH parameter change, but the residual-based CUSUM test is observed to be unsuitable for detecting changes in parameters belonging to ARMA part. The residual-based CUSUM test, however, outperforms the score test in testing for GARCH parameter change. A real data analysis is provided to illustrate the use of the proposed tests.

Suggested Citation

  • Song, Junmo & Kang, Jiwon, 2018. "Parameter change tests for ARMA–GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 41-56.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:41-56
    DOI: 10.1016/j.csda.2017.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317302578
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.12.002?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. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    2. Yoshiyuki Ninomiya, 2015. "Change-point model selection via AIC," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 943-961, October.
    3. Ilia Negri & Yoichi Nishiyama, 2017. "Z-process method for change point problems with applications to discretely observed diffusion processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 231-250, June.
    4. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    5. Hao Yu, 2007. "High Moment Partial Sum Processes of Residuals in ARMA Models and their Applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 72-91, January.
    6. Michael Robbins & Colin Gallagher & Robert Lund & Alexander Aue, 2011. "Mean shift testing in correlated data," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 498-511, September.
    7. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    8. 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.
    9. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    10. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    11. 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.
    12. 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.
    13. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Christopher Dienes & Alexander Aue, 2014. "On-Line Monitoring Of Pollution Concentrations With Autoregressive Moving Average Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 239-261, May.
    16. 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.
    17. Lee, O., 2013. "The functional central limit theorem for ARMA–GARCH processes," Economics Letters, Elsevier, vol. 121(3), pages 432-435.
    18. 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.
    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. Song, Junmo & Baek, Changryong, 2019. "Detecting structural breaks in realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 58-75.
    2. Bui, Anh Tuan & Apley, Daniel W., 2019. "An exploratory analysis approach for understanding variation in stochastic textured surfaces," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 33-50.

    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. 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.
    2. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1291-1320, October.
    3. Song, Junmo & Baek, Changryong, 2019. "Detecting structural breaks in realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 58-75.
    4. Christopher Dienes & Alexander Aue, 2014. "On-Line Monitoring Of Pollution Concentrations With Autoregressive Moving Average Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 239-261, May.
    5. Chunliang Deng & Xingfa Zhang & Yuan Li & Qiang Xiong, 2020. "Garch Model Test Using High-Frequency Data," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    6. Chang, Chia-Lin & Hsu, Hui-Kuang, 2013. "Modelling Volatility Size Effects for Firm Performance: The Impact of Chinese Tourists to Taiwan," MPRA Paper 45691, University Library of Munich, Germany.
    7. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR‐GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    8. M. Hashem Pesaran & Paolo Zaffaroni, 2004. "Model Averaging and Value-at-Risk Based Evaluation of Large Multi Asset Volatility Models for Risk Management," CESifo Working Paper Series 1358, CESifo.
    9. Chia-Lin Chang & Shu-Han Hsu & Michael McAleer, 2018. "An Event Study Analysis of Political Events, Disasters, and Accidents for Chinese Tourists to Taiwan," Sustainability, MDPI, vol. 10(11), pages 1-77, November.
    10. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2016. "Connecting VIX and Stock Index ETF," Tinbergen Institute Discussion Papers 16-010/III, Tinbergen Institute, revised 23 Jan 2017.
    11. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    12. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    13. Allen, David E. & Amram, Ron & McAleer, Michael, 2013. "Volatility spillovers from the Chinese stock market to economic neighbours," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 238-257.
    14. Massimiliano Caporin & Michael McAleer, 2011. "Thresholds, news impact surfaces and dynamic asymmetric multivariate GARCH," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(2), pages 125-163, May.
    15. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    16. Abdul Hakim & Michael McAleer, 2009. "VaR Forecasts and Dynamic Conditional Correlations for Spot and Futures Returns on Stocks and Bonds," CIRJE F-Series CIRJE-F-676, CIRJE, Faculty of Economics, University of Tokyo.
    17. Hakim, Abdul & McAleer, Michael, 2009. "Forecasting conditional correlations in stock, bond and foreign exchange markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2830-2846.
    18. Chang, C-L. & Hsu, S.-H. & McAleer, M.J., 2018. "An Event Study of Chinese Tourists to Taiwan," Econometric Institute Research Papers 2018-003/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    19. 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.
    20. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.

    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:csdana:v:121:y:2018:i:c:p:41-56. 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/locate/csda .

    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.