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A new Pearson-type QMLE for conditionally heteroskedastic models

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  • Zhu, Ke
  • Li, Wai Keung

Abstract

This paper proposes a novel Pearson-type quasi maximum likelihood estimator (QMLE) of GARCH($p, q$) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not the heavy-tailed but also the skewed innovations. Under the stationarity and weak moment conditions, the strong consistency and asymptotical normality of the PQMLE are obtained. With no further efforts, the PQMLE can apply to other conditionally heteroskedastic models. A simulation study is carried out to assess the performance of the PQMLE. Two applications to eight major stock indexes and four exchange rates further highlight the importance of our new method. To our best knowledge, the heavy-tailed and skewed innovations are observed together in practice, and the PQMLE now gives us a systematical way to capture this co-existing feature.

Suggested Citation

  • Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:52344
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    References listed on IDEAS

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    Cited by:

    1. Vijverberg, Chu-Ping C. & Vijverberg, Wim P.M. & Taşpınar, Süleyman, 2016. "Linking Tukey’s legacy to financial risk measurement," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 595-615.
    2. repec:eee:econom:v:202:y:2018:i:1:p:1-17 is not listed on IDEAS
    3. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.

    More about this item

    Keywords

    Asymmetric innovation; Conditionally heteroskedastic model; Exchange rates; GARCH model; Leptokurtic innovation; Non-Gaussian QMLE; Pearson's Type IV distribution; Pearsonian QMLE; Stock indexes.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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