Asymptotic properties of M-estimator for GARCH(1, 1) model parameters

DOI: https://doi.org/10.33581/2520-6508-2020-2-69-78

Abstract

GARCH(1,  1) model is used for analysis and forecasting of financial and economic time series. In the classical version, the maximum likelihood method is used to estimate the model parameters. However, this method is not convenient for analysis of models with residuals distribution different from normal. In this paper, we consider M-estimator for the GARCH(1,  1) model parameters, which is a generalization of the maximum likelihood method. An algorithm for constructing an M-estimator is described and its asymptotic properties are studied. A set of conditions is formulated under which the estimator is strictly consistent and has an asymptotically normal distribution. This method allows to analyze models with different residuals distributions; in particular, models with stable and tempered stable distributions that allow to take into account the features of real financial data: volatility clustering, heavy tails, asymmetry.

Author Biography

Uladzimir S. Tserakh, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

postgraduate student at the department of probability theory and mathematical statistics, faculty of applied mathematics and computer science

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Published
2020-07-30
Keywords: GARCH model, parameter estimation, consistency, asymptotic distribution, M-estimator
How to Cite
Tserakh, U. (2020). Asymptotic properties of M-estimator for GARCH(1, 1) model parameters. Journal of the Belarusian State University. Mathematics and Informatics, 2, 69-78. https://doi.org/10.33581/2520-6508-2020-2-69-78
Issue
No 2 (2020): Journal of the Belarusian State University. Mathematics and Informatics
Section
Probability Theory and Mathematical Statistics

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