Atlantis Press Paper Details: Convergence of GARCH Estimators: Theory and Empirical Evidence

The convergence of estimators, e.g., maximum likelihood estimators, for increasing sample size is well understood in many cases. However, even when the rate of convergence of the estimator is known, practical application is hampered by the fact, that the estimator cannot always be obtained at tenable computational cost. This paper combines the analysis of convergence of the estimator itself with the analysis of the convergence of stochastic optimization algorithms, e.g., threshold accepting, to the theoretical estimator. We discuss the joint convergence of estimator and algorithm in a formal framework. An application to a GARCH-model demonstrates the approach in practice by estimating actual rates of convergence through a large scale simulation study. Despite of the additional stochastic component introduced by the use of an optimization heuristic, the overall quality of the estimates turns out to be superior compared to conventional approaches.

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title:		Convergence of GARCH Estimators: Theory and Empirical Evidence
publication:		JCIS-2006 Proceedings
part of series:		Advances in Intelligent Systems Research
ISBN:		978-90-78677-01-7
ISSN:		1951-6851
DOI:		doi:10.2991/jcis.2006.94 (how to use a DOI)
author(s):		Dietmar Maringer, Peter Winker
corresponding author:		Dietmar Maringer
publication date:		October 2006
keywords:		GARCH, convergence, heuristic optimization, Threshold Accepting
abstract:		The convergence of estimators, e.g., maximum likelihood estimators, for increasing sample size is well understood in many cases. However, even when the rate of convergence of the estimator is known, practical application is hampered by the fact, that the estimator cannot always be obtained at tenable computational cost. This paper combines the analysis of convergence of the estimator itself with the analysis of the convergence of stochastic optimization algorithms, e.g., threshold accepting, to the theoretical estimator. We discuss the joint convergence of estimator and algorithm in a formal framework. An application to a GARCH-model demonstrates the approach in practice by estimating actual rates of convergence through a large scale simulation study. Despite of the additional stochastic component introduced by the use of an optimization heuristic, the overall quality of the estimates turns out to be superior compared to conventional approaches.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		JCIS06-CIEF-227.pdf (54 K)