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  • Yu-Ning Li (a1), Yi Zhang (a1) and Caiya Zhang (a2)

This article investigates the statistical inference problem of whether a measurement equation is self-consistent in the logarithmic realized GARCH model (log-RealGARCH). First, we provide the sufficient and necessary conditions for the strict stationarity of both the log-RealGARCH model and the log-GARCH-X model. Under these conditions, strong consistency and asymptotic normality of the quasi-maximum likelihood estimators of these two models are obtained. Then, based on the asymptotic results, we propose a Hausman-type self-consistency test for diagnosing the suitability of the measurement equation in the log-RealGARCH model. Finally, the results of simulations and an empirical study are found to accord with the theoretical results.

Corresponding author
*Address correspondence to Yi Zhang, School of Mathematical Sciences, Zhejiang University, Hangzhou, China; e-mail:
Caiya Zhang, Department of Statistics, Zhejiang University City College, Hangzhou, China; e-mail:
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We especially thank two anonymous referees and Pentti Saikkonen, the co-editor, for helpful suggestions that greatly improved the article. We are also grateful for the comments from seminar and conference participants at the 2nd International Symposium on Interval Data Modelling: Theory and Applications (SIDM2016) and Contributed Sessions in Statistics (CSS09) of 2017 IMS-China International Conference on Statistics and Probability. This research is partly supported by the Zhejiang Provincial Natural Science Foundation (No. LY18A010005), the Research Project of Humanities and Social Science of Ministry of Education of China (No. 17YJA910003), the Fundamental Research Funds for the Central Universities and Major Project of the National Social Science Foundation of China (No.13&ZD163).

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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