Convergence of GARCH Estimators: Theory and Empirical Evidence

DOI

10.2991/jcis.2006.94How to use a DOI?

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

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Dietmar Maringer
AU  - Peter Winker
PY  - 2006/10
DA  - 2006/10
TI  - Convergence of GARCH Estimators: Theory and Empirical Evidence
BT  - Proceedings of the 9th Joint International Conference on Information Sciences (JCIS-06)
PB  - Atlantis Press
SN  - 1951-6851
UR  - https://doi.org/10.2991/jcis.2006.94
DO  - 10.2991/jcis.2006.94
ID  - Maringer2006/10
ER  -