Picture of athlete cycling

Open Access research with a real impact on health...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

Explore open research content by Physical Activity for Health...

Estimation for a non-stationary semi-strong GARCH(1,1) model with heavy-tailed errors

Linton, O. and Pan, J. and Wang, H. (2010) Estimation for a non-stationary semi-strong GARCH(1,1) model with heavy-tailed errors. Econometric Theory, 26 (1). pp. 1-28. ISSN 0266-4666

[img]
Preview
Text (strathprints013647)
strathprints013647.pdf - Accepted Author Manuscript

Download (301kB) | Preview

Abstract

This paper studies the estimation of a semi-strong GARCH(1,1) model when it does not have a stationary solution, where semi-strong means that we do not require the errors to be independent over time. We establish necessary and su±cient conditions for a semi-strong GARCH(1,1) process to have a unique stationary solution. For the non-stationary semi-strong GARCH(1,1) model, we prove that a local minimizer of the least absolute deviations (LAD) criterion converges at the rate p n to a normal distribution under very mild moment conditions for the errors. Furthermore, when the distributions of the errors are in the domain of attraction of a stable law with the exponent · 2 (1; 2), it is shown that the asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is non-Gaussian but is some stable law with the exponent · 2 (0; 2). The asymptotic distribution is di±cult to estimate using standard parametric methods. Therefore, we propose a percentile-t subsampling bootstrap method to do inference when the errors are independent and identically distributed, as in Hall and Yao (2003). Our result implies that the least absolute deviations estimator (LADE) is always asymptotically normal regardless of whether there exists a stationary solution or not even when the errors are heavy-tailed. So the LADE is more appealing when the errors are heavy-tailed. Numerical results lend further support to our theoretical results.