Asymptotic properties of M-estimator for GARCH(1, 1) model parameters
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 no...
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Online Access: | https://journals.bsu.by/index.php/mathematics/article/view/2971 |
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doaj-9a1628f9460343b1b0297499af63bb9b2020-12-10T17:28:41ZbelBelarusian State University Журнал Белорусского государственного университета: Математика, информатика 2520-65082617-39562020-07-012697810.33581/2520-6508-2020-2-69-782971Asymptotic properties of M-estimator for GARCH(1, 1) model parametersUladzimir S. Tserakh0https://orcid.org/0000-0003-0034-7672Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, BelarusGARCH(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.https://journals.bsu.by/index.php/mathematics/article/view/2971garch modelparameter estimationconsistencyasymptotic distributionm-estimator |
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Belarusian |
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Article |
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DOAJ |
author |
Uladzimir S. Tserakh |
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Uladzimir S. Tserakh Asymptotic properties of M-estimator for GARCH(1, 1) model parameters Журнал Белорусского государственного университета: Математика, информатика garch model parameter estimation consistency asymptotic distribution m-estimator |
author_facet |
Uladzimir S. Tserakh |
author_sort |
Uladzimir S. Tserakh |
title |
Asymptotic properties of M-estimator for GARCH(1, 1) model parameters |
title_short |
Asymptotic properties of M-estimator for GARCH(1, 1) model parameters |
title_full |
Asymptotic properties of M-estimator for GARCH(1, 1) model parameters |
title_fullStr |
Asymptotic properties of M-estimator for GARCH(1, 1) model parameters |
title_full_unstemmed |
Asymptotic properties of M-estimator for GARCH(1, 1) model parameters |
title_sort |
asymptotic properties of m-estimator for garch(1, 1) model parameters |
publisher |
Belarusian State University |
series |
Журнал Белорусского государственного университета: Математика, информатика |
issn |
2520-6508 2617-3956 |
publishDate |
2020-07-01 |
description |
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. |
topic |
garch model parameter estimation consistency asymptotic distribution m-estimator |
url |
https://journals.bsu.by/index.php/mathematics/article/view/2971 |
work_keys_str_mv |
AT uladzimirstserakh asymptoticpropertiesofmestimatorforgarch11modelparameters |
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1724387287584735232 |