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Adaptive quasi-maximum likelihood estimation of GARCH models with Student’s t likelihood

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  • Xiaorui Zhu
  • Li Xie

Abstract

This paper proposes an adaptive quasi-maximum likelihood estimation (QMLE) when forecasting the volatility of financial data with the generalized autoregressive conditional heteroscedasticity (GARCH) model. When the distribution of volatility data is unspecified or heavy-tailed, we worked out adaptive QMLE based on data by using the scale parameter ηf to identify the discrepancy between wrongly specified innovation density and the true innovation density. With only a few assumptions, this adaptive approach is consistent and asymptotically normal. Moreover, it gains better efficiency under the condition that innovation error is heavy-tailed. Finally, simulation studies and an application show its advantage.

Suggested Citation

  • Xiaorui Zhu & Li Xie, 2016. "Adaptive quasi-maximum likelihood estimation of GARCH models with Student’s t likelihood," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(20), pages 6102-6111, October.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:20:p:6102-6111
    DOI: 10.1080/03610926.2014.957852
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