IDEAS home Printed from https://ideas.repec.org/p/ihs/ihsesp/156.html
   My bibliography  Save this paper

The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification. A Monte Carlo Study

Author

Listed:
  • Caporale, Guglielmo Maria

    (London South Bank University)

  • Ntantamis, Christos

    (University of Piraeus)

  • Pantelidis, Theologos

    (University of Piraeus)

  • Pittis, Nikitas

    (University of Piraeus)

Abstract

In this study, we examine the Brock, Dechert and Scheinkman (BDS) test when applied to the standardised residuals of an estimated GARCH(1,1) model as a test for the adequacy of this specification. We review the conditions derived by De Lima (1996, Econometric Reviews, 15, 237-259) for the nuisance-parameter free property to hold, and address the issue of their necessity, using the GARCH(1,1) model. By means of Monte Carlo simulations, we show that, provided that the unconditional mean exists, the BDS test statistic still approximates the standard null distribution even when the majority of the conditions are violated. Further, the test performs reasonably well, as its empirical size is rather close to the nominal one. As a by-product of this study, we also examine the related issue of consistency of the QML estimators of the conditional variance parameters under various parameter configurations and alternative distributional assumptions on the innovation process.

Suggested Citation

  • Caporale, Guglielmo Maria & Ntantamis, Christos & Pantelidis, Theologos & Pittis, Nikitas, 2004. "The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification. A Monte Carlo Study," Economics Series 156, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:156
    as

    Download full text from publisher

    File URL: https://irihs.ihs.ac.at/id/eprint/1567
    File Function: First version, 2004
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
    2. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    3. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    4. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, March.
    5. He, Changli & Teräsvirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(6), pages 824-846, December.
    6. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
    9. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Geoff Willcocks, 2009. "UK Housing Market: Time Series Processes with Independent and Identically Distributed Residuals," The Journal of Real Estate Finance and Economics, Springer, vol. 39(4), pages 403-414, November.
    2. Mayer, Alexander & Wied, Dominik, 2023. "Estimation and inference in factor copula models with exogenous covariates," Journal of Econometrics, Elsevier, vol. 235(2), pages 1500-1521.
    3. Isao Ishida & Toshiaki Watanabe, 2009. "Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model," CIRJE F-Series CIRJE-F-608, CIRJE, Faculty of Economics, University of Tokyo.
    4. Borusyak, K., 2011. "Nonlinear Dynamics of the Russian Stock Market in Problems of Risk Management," Journal of the New Economic Association, New Economic Association, issue 11, pages 85-105.
    5. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    6. Emilian DOBRESCU, 2016. "Controversies over the Size of the Public Budget," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 5-34, December.
    7. Jorge Pérez-Rodríguez & Julián Andrada-Félix, 2013. "Estimating critical values for testing the i.i.d. in standardized residuals from GARCH models in finite samples," Computational Statistics, Springer, vol. 28(2), pages 701-734, April.
    8. Halil Guler & Anil Talasli, 2010. "Modelling the Daily Currency in Circulation in Turkey," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 10(1), pages 29-46.
    9. Samet G nay, 2015. "Chaotic Structure of the BRIC Countries and Turkey's Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 5(2), pages 515-522.

    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. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, Osaka University.
    2. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    3. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    4. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    5. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, "undated". "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, Department of Economics and Business Economics, Aarhus University.
    6. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    7. Feng, Yuanhua & Härdle, Wolfgang Karl, 2020. "A data-driven P-spline smoother and the P-Spline-GARCH models," IRTG 1792 Discussion Papers 2020-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Berkes, István & Hörmann, Siegfried & Horváth, Lajos, 2008. "The functional central limit theorem for a family of GARCH observations with applications," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2725-2730, November.
    9. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    10. E. Ruiz & M.A. Carnero & D. Pereira, 2004. "Effects of Level Outliers on the Identification and Estimation of GARCH Models," Econometric Society 2004 Australasian Meetings 21, Econometric Society.
    11. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, January.
    12. Chu, L. & McAleer, M.J. & Chen, C-C., 2009. "How Volatile is ENSO?," Econometric Institute Research Papers EI 2009-18, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
    14. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    15. Li, Dong & Li, Muyi & Wu, Wuqing, 2014. "On dynamics of volatilities in nonstationary GARCH models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 86-90.
    16. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    17. Han, Heejoon & Park, Joon Y., 2012. "ARCH/GARCH with persistent covariate: Asymptotic theory of MLE," Journal of Econometrics, Elsevier, vol. 167(1), pages 95-112.
    18. Chang, Chia-Lin, 2015. "Modelling a latent daily Tourism Financial Conditions Index," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 113-126.
    19. Emma Iglesias & Jean Marie Dufour, 2004. "Finite Sample and Optimal Inference in Possibly Nonstationary ARCH Models with Gaussian and Heavy-Tailed Errors," Econometric Society 2004 North American Summer Meetings 161, Econometric Society.
    20. HAFNER, Christian & PREMINGER, Arie, 2016. "On Asymptotic Theory for ARCH(infinite) Models," LIDAM Discussion Papers CORE 2016030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    BDS Test; Nuisance-Parameter Free Property; Monte Carlo Analysis; GARCH(1; 1) Model; QML estimator;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    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:ihs:ihsesp:156. 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: Doris Szoncsitz (email available below). General contact details of provider: https://edirc.repec.org/data/deihsat.html .

    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.