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

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. Und...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2020-12, Vol.61 (6), p.2313-2330
Main Authors: Zhang, Caiya, Xu, Kaihong, Qian, Lianfen
Format: Article
Language:English
Subjects:
Asymptotic properties
Economic models
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Estimating techniques
Finance
Insurance
Management
Mathematics and Statistics
Maximum likelihood estimation
Normality
Operations Research/Decision Theory
Parameter estimation
Probability Theory and Stochastic Processes
Regular Article
Statistics
Statistics for Business
Volatility
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Summary: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 ).
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-018-1051-8