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LARGE SAMPLE DISTRIBUTION OF WEIGHTED SUMS OF ARCH(p) SQUARED RESIDUAL CORRELATIONS

Author

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  • Horváth, Lajos
  • Kokoszka, Piotr

Abstract

We develop asymptotic theory for linear statistics of sample autocorrelations of squared residuals from an ARCH(p) model. Our results are valid for most estimators used in practice and do not depend on the assumption of normality of the errors; the existence of the fourth moment is required. In several special cases, we identify the limit distributions as well-known functionals of a Brownian motion.

Suggested Citation

  • Horváth, Lajos & Kokoszka, Piotr, 2001. "LARGE SAMPLE DISTRIBUTION OF WEIGHTED SUMS OF ARCH(p) SQUARED RESIDUAL CORRELATIONS," Econometric Theory, Cambridge University Press, vol. 17(2), pages 283-295, April.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:02:p:283-295_17
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    Citations

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    Cited by:

    1. Zhu, Fukang & Wang, Dehui, 2010. "Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 496-508, February.
    2. Andreou, Elena & Werker, Bas J.M., 2015. "Residual-based rank specification tests for AR–GARCH type models," Journal of Econometrics, Elsevier, vol. 185(2), pages 305-331.
    3. repec:hal:journl:peer-00732536 is not listed on IDEAS
    4. Francq, Christian & Zakoïan, Jean-Michel, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Journal of Econometrics, Elsevier, vol. 159(1), pages 151-165, November.
    5. 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.
    6. Andreou, E. & Werker, B.J.M., 2004. "An Alternative Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2004-56, Tilburg University, Center for Economic Research.
    7. Elena Andreou & Bas J.M. Werker, 2014. "Residual-based Rank Specification Tests for AR-GARCH type models," University of Cyprus Working Papers in Economics 02-2014, University of Cyprus Department of Economics.
    8. Christian FRANCQ & Jean-Michel ZAKOIAN, 2009. "Properties of the QMLE and the Weighted LSE for LARCH(q) Models," Working Papers 2009-19, Center for Research in Economics and Statistics.
    9. Werker, Bas J M & Andreou, Elena, 2013. "Residual-based Rank Specification Tests for AR-GARCH type models," CEPR Discussion Papers 9583, C.E.P.R. Discussion Papers.
    10. Andreou, E. & Werker, B.J.M., 2004. "An Alternative Asymptotic Analysis of Residual-Based Statistics," Other publications TiSEM 93fe16c1-9f21-4dab-9b73-4, Tilburg University, School of Economics and Management.
    11. Berkes, István & Horváth, Lajos, 2003. "Limit results for the empirical process of squared residuals in GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 271-298, June.
    12. Ghoudi, Kilani & Rémillard, Bruno, 2014. "Comparison of specification tests for GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 291-300.
    13. Andreou, E. & Werker, B.J.M., 2003. "A Simple Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2003-118, Tilburg University, Center for Economic Research.
    14. Andreou, E. & Werker, B.J.M., 2003. "A Simple Asymptotic Analysis of Residual-Based Statistics," Other publications TiSEM 9fe68e51-a026-4660-b6e7-8, Tilburg University, School of Economics and Management.

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