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Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic models

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  • Francq, Christian
  • Zakoian, Jean-Michel

Abstract

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be zero and to reach its minimum for non-zero innovations, and is appropriate for long-memory modeling when infinite orders are allowed. It is shown that the quasi-maximum likelihood estimator is, in general, inconsistent. To solve this problem, we propose a self-weighted least-squares estimator and show that this estimator is asymptotically normal. Furthermore, a score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. The latter have an asymptotic distribution which is far from the standard chi-square. Simulation experiments are carried out to assess the performance of the proposed estimator.

Suggested Citation

  • Francq, Christian & Zakoian, Jean-Michel, 2009. "Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic models," MPRA Paper 15147, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:15147
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    File URL: https://mpra.ub.uni-muenchen.de/15147/1/MPRA_paper_15147.pdf
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    References listed on IDEAS

    as
    1. Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Conditional homoscedasticity testing; Inconsistent estimator; Leverage effect; Linear ARCH; Quasi-maximum likelihood; Weighted least-squares;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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