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

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  • Guglielmo Maria Caporale

Abstract

In this study we examine the widely used Brock, Dechert, and Scheinkman (BDS) test when applied to the logarithm of the squared standardized 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 flexible framework offered by the GARCH(1,1) model in terms of moment, memory, and time heterogeneity properties. By means of Monte Carlo simulations, we show that the BDS test statistic still approximates the standard null distribution even for mildly explosive processes that violate the majority of the conditions. Thus the test performs reasonably well, its empirical size being rather close to the nominal one. As a by-product of this study, we also shed light on the related issue of the consistency of the QML estimators of the conditional variance parameters under various parameter configurations and alternative distributional assumptions on the innovation process. Copyright 2005, Oxford University Press.

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  • Guglielmo Maria Caporale, 2005. "The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 282-309.
    • Handle: RePEc:oup:jfinec:v:3:y:2005:i:2:p:282-309
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    1. Shiqing Ling & Michael McAleer, 2001. "Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models," ISER Discussion Paper 0534, Institute of Social and Economic Research, The University of Osaka.
    2. 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.
    3. 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.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    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.

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    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

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