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STATISTICAL INFERENCE FOR MEASUREMENT EQUATION SELECTION IN THE LOG-REALGARCH MODEL

Yu-Ning Li, Yi Zhang and Caiya Zhang

Econometric Theory, 2019, vol. 35, issue 5, 943-977

Abstract: 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.

Date: 2019
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