Properties and estimation of garch(1,1) model

Abstract

We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-tailed. We investigate the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1,1) model. A boundedconditional fourth moment of the rescaled variable (the ratio of the disturbance to the conditional standard deviation) is sufficient for the result. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.

Keywords

Modeli;

Data

Language:	English
Year of publishing:	2005
Typology:	1.01 - Original Scientific Article
Organization:	UL FDV - Faculty of Social Sciences
Publisher:	Fakulteta za družbene vede
UDC:	303
COBISS:	24315997
ISSN:	1854-0023
Views:	653
Downloads:	121
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary keywords:	Models;
URN:	URN:NBN:SI
Type (COBISS):	Not categorized
Pages:	str. 243-257
Volume:	2
Issue:	ǂno. ǂ2
Chronology:	2005
Keywords (UDC):	social sciences;družbene vede;methods of the social sciences;metode družbenih ved;
ID:	1467971