ARCH/GARCH with persistent covariate: Asymptotic theory of MLE

Heejoon Han and Joon Y. Park

Journal of Econometrics, 2012, vol. 167, issue 1, 95-112

Abstract: The paper considers a volatility model which introduces a persistent, integrated or near-integrated, covariate to the standard GARCH(1, 1) model. For such a model, we derive the asymptotic theory of the quasi-maximum likelihood estimator. In particular, we establish consistency and obtain limit distribution. The limit distribution is generally non-Gaussian and represented as a functional of Brownian motions. However, it becomes Gaussian if the covariate has innovation uncorrelated with the squared innovation of the model or the volatility function is linear in parameter. We provide a simulation study to demonstrate the relevance and usefulness of our asymptotic theory.

Keywords: ARCH; GARCH; Persistent covariate; Maximum likelihood estimator; Asymptotic distribution theory (search for similar items in EconPapers)
JEL-codes: C22 C50 G12 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:167:y:2012:i:1:p:95-112

DOI: 10.1016/j.jeconom.2011.10.004

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