Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates

Arbeitspapier

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 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 t-statistics following standard Normal distributions in large sample irrespective of whether the regressor is stationary or not.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: cemmap working paper ; No. CWP18/13

Classification and Topics

• Classification: Wirtschaft

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Han, Heejoon ; Kristensen, Dennis
• Event: Veröffentlichung
• (who): Centre for Microdata Methods and Practice (cemmap)
• (where): London
• (when): 2013

Further information

• DOI: doi:10.1920/wp.cem.2013.1813
• Handle: http://hdl.handle.net/10419/79507
• Last update: 10.03.2025, 11:43 AM CET