A new Pearson-Type QMLE for conditionally heteroscedastic models

Ke ZHU, Wai Keung LI

Research output: Contribution to journalArticlespeer-review

16 Citations (Scopus)


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. Copyright © 2015 American Statistical Association.
Original languageEnglish
Pages (from-to)552-565
JournalJournal of Business and Economic Statistics
Issue number4
Early online dateOct 2015
Publication statusPublished - 2015


Zhu, K., & Li, W. K. (2015). A new Pearson-Type QMLE for conditionally heteroscedastic models. Journal of Business & Economic Statistics, 33(4), 552-565. doi: 10.1080/07350015.2014.977446


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


Dive into the research topics of 'A new Pearson-Type QMLE for conditionally heteroscedastic models'. Together they form a unique fingerprint.