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The Effect of (Mis-Specified) GARCH Filters on the Finite Sample Distribution of the BDS Test

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  • Brooks, Chris
  • Heravi, Saeed M

Abstract

This paper considers the effect of using a GARCH filter on the properties of the BDS test statistic as well as a number of other issues relating to the application of the test. It is found that, for certain values of the user-adjustable parameters, the finite sample distribution of the test is far-removed from asymptotic normality. In particular, when data generated from some completely different model class are filtered through a GARCH model, the frequency of rejection of iid falls, often substantially. The implication of this result is that it might be inappropriate to use non-rejection of iid of the standardised residuals of a GARCH model as evidence that the GARCH model 'fits' the data. Citation Copyright 1999 by Kluwer Academic Publishers.

Suggested Citation

  • Brooks, Chris & Heravi, Saeed M, 1999. "The Effect of (Mis-Specified) GARCH Filters on the Finite Sample Distribution of the BDS Test," Computational Economics, Springer;Society for Computational Economics, vol. 13(2), pages 147-162, April.
    • Handle: RePEc:kap:compec:v:13:y:1999:i:2:p:147-62
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    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. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
    3. Yi-Ting Chen & Chung-Ming Kuan, 2002. "Time irreversibility and EGARCH effects in US stock index returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 565-578.
    4. Brooks, Chris & Henry, Olan T., 2000. "Linear and non-linear transmission of equity return volatility: evidence from the US, Japan and Australia," Economic Modelling, Elsevier, vol. 17(4), pages 497-513, December.
    5. Yao, Can-Zhong & Lin, Qing-Wen, 2017. "Recurrence plots analysis of the CNY exchange markets based on phase space reconstruction," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 584-596.
    6. Brooks, Chris & Henry, Olan T., 2000. "Can portmanteau nonlinearity tests serve as general mis-specification tests?: Evidence from symmetric and asymmetric GARCH models," Economics Letters, Elsevier, vol. 67(3), pages 245-251, June.
    7. Evzen Kocenda & Lubos Briatka, 2004. "Advancing the iid Test Based on Integration across the Correlation Integral: Ranges, Competition, and Power," CERGE-EI Working Papers wp235, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    8. Fernandes, Marcelo & Preumont, Pierre-Yves, 2012. "The Finite-Sample Size of the BDS Test for GARCH Standardized Residuals," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 32(2), April.
    9. Wen Cheong, Chin & Hassan Shaari Mohd Nor, Abu & Isa, Zaidi, 2007. "Asymmetry and long-memory volatility: Some empirical evidence using GARCH," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 651-664.
    10. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    11. Theodore Panagiotidis, 2002. "Testing the assumption of Linearity," Economics Bulletin, AccessEcon, vol. 3(29), pages 1-9.
    12. 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.
    13. Dungey, Mardi & Milunovich, George & Thorp, Susan, 2010. "Unobservable shocks as carriers of contagion," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 1008-1021, May.
    14. Theodore Panagiotidis, 2005. "Market capitalization and efficiency. Does it matter? Evidence from the Athens Stock Exchange," Applied Financial Economics, Taylor & Francis Journals, vol. 15(10), pages 707-713.
    15. Mircea Cristian Gherman, 2011. "Analysis of GARCH Modeling in Financial Markets: An Approach Based on Technical Analysis Strategies," Acta Universitatis Danubius. OEconomica, Danubius University of Galati, issue 4(4), pages 158-171, August.
    16. repec:ebl:ecbull:v:3:y:2002:i:29:p:1-9 is not listed on IDEAS
    17. K.P. Lim & M.J. Hinich & K.S. Liew, 2003. "GARCH Diagnosis with Portmanteau Bicorrelation Test: An Application on the Malaysia's Stock Market," Finance 0307013, University Library of Munich, Germany.
    18. Evzen Kocenda & Lubos Briatka, 2005. "Optimal Range for the iid Test Based on Integration Across the Correlation Integral," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 265-296.
    19. Khanday, Ishfaq Nazir & Tarique, Md., 2023. "Does income inequality respond asymmetrically to financial development? Evidence from India using asymmetric cointegration and causality tests," The Journal of Economic Asymmetries, Elsevier, vol. 28(C).

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