Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates

A-Tier
Journal: Journal of Business & Economic Statistics
Year: 2014
Volume: 32
Issue: 3
Pages: 416-429

Score contribution per author:

2.011 = (α=2.01 / 2 authors) × 2.0x A-tier

α: calibrated so average coauthorship-adjusted count equals average raw count

Abstract

This article 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 <italic>d<sub>x</sub></italic>; in particular, we allow for both stationary and nonstationary covariates. We show that the QMLE's of the parameters entering the volatility equation are consistent and mixed-normally distributed in large samples. The convergence rates and limiting distributions of the QMLE's depend on whether the regressor is stationary or not. However, standard inferential tools for the parameters are robust to the level of persistence of the regressor with <italic>t</italic>-statistics following standard Normal distributions in large sample irrespective of whether the regressor is stationary or not. Supplementary materials for this article are available online.

Technical Details

RePEc Handle
repec:taf:jnlbes:v:32:y:2014:i:3:p:416-429
Journal Field
Econometrics
Author Count
2
Added to Database
2026-01-25