Open AccessAsymptotic properties of M-estimator for GARCH(1, 1) model parameters
Author(s) -
Uladzimir S. Tserakh
Publication year - 2020
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika/žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-3956
pISSN - 2520-6508
DOI - 10.33581/2520-6508-2020-2-69-78
Subject(s) - estimator , mathematics , autoregressive conditional heteroskedasticity , generalization , volatility (finance) , financial models with long tailed distributions and volatility clustering , volatility clustering , asymptotic distribution , series (stratigraphy) , econometrics , statistics , stochastic volatility , sabr volatility model , mathematical analysis , paleontology , biology
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.