Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Non-Stationary Covariates

Heejoon Han and Dennis Kristensen

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: This paper investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE?s) of the GARCH model augmented by including an additional explanatory variable - the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as captured by its long-memory parameter dx; in particular, we allow for both stationary and non-stationary covariates. We show that the QMLE'?s of the regression coefficients entering the volatility equation are consistent and normally distributed in large samples independently of the degree of persistence. This implies that standard inferential tools, such as t-statistics, do not have to be adjusted to the level of persistence. On the other hand, the intercept in the volatility equation is not identifi?ed when the covariate is non-stationary which is akin to the results of Jensen and Rahbek (2004, Econometric Theory 20) who develop similar results for the pure GARCH model with explosive volatility.

Keywords: GARCH; Persistent covariate; Fractional integration; Quasi-maximum likelihood estimator; Asymptotic distribution theory. (search for similar items in EconPapers)
JEL-codes: C22 C50 G12 (search for similar items in EconPapers)
Pages: 28 Heejoon Han and Dennis Kristensen
Date: 2012-05-18
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-ore and nep-sea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://repec.econ.au.dk/repec/creates/rp/12/rp12_25.pdf (application/pdf)

Related works:
Journal Article: Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates (2014)
Working Paper: Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates (2013)
Working Paper: Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates (2013)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2012-25

Access Statistics for this paper

More papers in CREATES Research Papers from Department of Economics and Business Economics, Aarhus University
Bibliographic data for series maintained by ().