scholarly journals Testing Over-Identifying Restrictions Without Consistent Estimation of the Asymptotic Covariance Matrix

2009 ◽  
Author(s):  
Wei-Ming Lee ◽  
Chung-Ming Kuan
Keyword(s):  
Covariance Matrix ◽  
Asymptotic Covariance Matrix ◽  
Consistent Estimation ◽  
Asymptotic Covariance

scholarly journals Properties and estimation of GARCH(1,1) model

2005 ◽  
Vol 2 (2) ◽  
Author(s):  
Petra Posedel
Keyword(s):  
Fourth Moment ◽  
Asymptotic Covariance Matrix ◽  
Likelihood Estimator ◽  
Consistent Estimation ◽  
Strong Stationarity ◽  
Asymptotic Covariance ◽  
Sampling Behavior ◽  
Garch Processes ◽  
Heavy Tailed ◽  
Quasi Maximum Likelihood

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 bounded conditional 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.

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