Asymptotic properties of the QMLE in a log-linear RealGARCH model with Gaussian errors

  • Caiya Zhang
  • Kaihong Xu
  • Lianfen QianEmail author
Regular Article


To incorporate the realized volatility in stock return, Hansen et al. (J Appl Econ 27:877–906, 2012) proposed a RealGARCH model and conjectured some theoretical properties about the quasi-maximum likelihood estimation (QMLE) for parameters in a log-linear RealGARCH model without rigorous proof. Under Gaussian errors, this paper derives the detailed proof of the theoretical results including consistency and asymptotic normality of the QMLE, hence it solves the conjectures in Hansen et al. (J Appl Econ 27:877–906, 2012).


RealGARCH model Quasi-maximum likelihood estimator Consistency and asymptotic normality 



We thank the Editor-in-Chief and the two referees for their helpful comments and suggestions that have led to significant improvements of this paper. Caiya Zhang’s research is partially supported by the Research Projects of Humanities and Social Science of Ministry of Education of China (17YJA910003), Intelligent Plant Factory of Zhejiang Province Engineering Lab. Lianfen Qian’s research is partially supported by the Natural Science Foundation of Zhejiang Province (LY17A010012) and the OURI Curriculum Grant from Florida Atlantic University, USA.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer and Computing ScienceZhejiang University City CollegeHangzhouChina
  2. 2.Department of Mathematical SciencesFlorida Atlantic UniversityBoca RatonUSA

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