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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 just the heavy-tailed but also the skewed innovations. Under strict stationarity and some 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. Heavy-tailed and skewed innovations are often observed together in practice, and the PQMLE now gives us a systematical way to capture these two co-existing features.

Suggested Citation

  • Zhu, Ke & Li, Wai Keung, 2014. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52732, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:52732
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    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.;
    All these keywords.

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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