A New Pearson-Type QMLE for Conditionally Heteroscedastic Models

This article 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 innovatio...

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Bibliographic Details
Published inJournal of business & economic statistics Vol. 33; no. 4; pp. 552 - 565
Main Authors Zhu, Ke, Li, Wai Keung
Format Journal Article
LanguageEnglish
Published Alexandria Taylor & Francis 02.10.2015
American Statistical Association
Taylor & Francis Ltd
Subjects
Asymmetric innovation
Conditionally heteroscedastic model
Economic models
Exchange rates
Foreign exchange rates
GARCH model
Indexes
Leptokurtic innovation
Maximum likelihood method
Non-Gaussian QMLE
Pearson's Type IV distribution
Pearsonian QMLE
Stock indexes
Studies
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Summary:This article 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 asymptotic normality of the PQMLE are obtained. With no further efforts, the PQMLE can be applied to other conditionally heteroscedastic models. A simulation study is carried out to assess the performance of the PQMLE. Two applications to four major stock indexes and two 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 systematic way to capture these two coexisting features.
ISSN:0735-0015
1537-2707
DOI:10.1080/07350015.2014.977446