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Volatility Modeling with Leverage Effect under Laplace Errors


  • Jiang Zhengjun

    (Bryant College, Beijing Institute of Technology, Zhuhai, No. 6, Jinfeng Road, Tangjiawan, Zhuhai, Guangdong519088, China.)

  • Xia Weixuan

    (Mathematical Finance Program, Boston University Questrom School of Business, 595 Commonwealth Avenue, Boston, MA 02215, USA.)


This paper discusses four GARCH-type models (A-GARCH, NA-GARCH, GJR-GARCH, and E-GARCH) in representing volatility of financial returns with leverage effect. In these models, errors are assumed to follow a Laplace distribution in order to deal with the typical leptokurtic feature of financial returns. The properties of these models are analyzed theoretically in terms of unconditional variance, kurtosis, autocorrelation function and news impact, and are further examined in the applications to real financial time series. Comparison is made with other choices of error distributions such as normal, Student-5, and Student-7 distributions, respectively. We also conduct residual analyses to justify the choice of error distributions and find that Laplace-E-GARCH model still performs very well. Our main purpose is to study and compare the proposed models’ relative adequacies and underlying limitations.

Suggested Citation

  • Jiang Zhengjun & Xia Weixuan, 2018. "Volatility Modeling with Leverage Effect under Laplace Errors," Journal of Time Series Econometrics, De Gruyter, vol. 10(1), pages 1-29, January.
  • Handle: RePEc:bpj:jtsmet:v:10:y:2018:i:1:p:29:n:3
    DOI: 10.1515/jtse-2016-0019

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