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GARCH models without positivity constraints: Exponential or log GARCH?

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  • Francq, Christian
  • Wintenberger, Olivier
  • Zakoïan, Jean-Michel

Abstract

This paper provides a probabilistic and statistical comparison of the log-GARCH and EGARCH models, which both rely on multiplicative volatility dynamics without positivity constraints. We compare the main probabilistic properties (strict stationarity, existence of moments, tails) of the EGARCH model, which are already known, with those of an asymmetric version of the log-GARCH. The quasi-maximum likelihood estimation of the log-GARCH parameters is shown to be strongly consistent and asymptotically normal. Similar estimation results are only available for the EGARCH (1,1) model, and under much stronger assumptions. The comparison is pursued via simulation experiments and estimation on real data.

Suggested Citation

  • Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    • Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:34-46
    DOI: 10.1016/j.jeconom.2013.05.004
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    More about this item

    Keywords

    EGARCH; Log-GARCH; Quasi-maximum likelihood; Strict stationarity; Tail index;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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