Calzolari, Giorgio and Fiorentini, Gabriele and Panattoni, Lorenzo (1993): Alternative estimators of the covariance matrix in GARCH models. Published in: Universita' di Messina, Istituto di Economia, Statistica e Analisi del Territorio No. Quaderno No. 11 (1993): pp. 133.

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Abstract
With most of the available software packages, estimates of the parameter covariance matrix in a GARCH model are usually obtained from the outer products of the first derivatives of the loglikelihoods (BHHH estimator). However, other estimators could be defined and used, analogous to the covariance matrix estimators in maximum likelihood studies described in the literature for other types of models (linear regression model, linear and nonlinear simultaneous equations, Probit and Tobit models). These alternative estimators can be derived from: (1) the Hessian (observed information), (2) the estimated information (expected Hessian), (3) a mixture of Hessian and outer products matrix (White's QML covarjance matrix). Signifacant differences among these estimates can be interpreted as an indication of misspecification, or can be due to systematic inequalities between alternative estimators in small samples. Unlike other types of models, from our Monte Carlo study we do not encounter very large differences, presumably because GARCH estimation is usually applied when the sample size is rather large. However, analogously to otber types of models we find in this Monte Carlo study that, even in absence of misspecification, the sign of the differences between some estimators is almost systematic. This suggests that, as for other types of models, the choice of the covariance estimator is not neutral, but the results of hypotheses testing are not strongly affected by such a choice.
Item Type:  MPRA Paper 

Original Title:  Alternative estimators of the covariance matrix in GARCH models 
Language:  English 
Keywords:  GARCH model; Hessian matrix; outer products; maximum likelihood 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  24433 
Depositing User:  Giorgio Calzolari 
Date Deposited:  16. Aug 2010 11:51 
Last Modified:  12. Feb 2013 20:39 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/24433 