To read the full version of this content please select one of the options below:

A Simple Efficient Moment-based Estimator for the Stochastic Volatility Model

aMcGill University, and Centre interuniversitaire de recherche en analyse des organisations (CIRANO), Canada
bMcGill University, Centre interuniversitaire de recherche en analyse des organisations (CIRANO), and Centre interuniversitaire de recherche en économie quantitative (CIREQ), Canada

Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A

ISBN: 978-1-78973-242-9, eISBN: 978-1-78973-241-2

ISSN: 0731-9053

Publication date: 30 August 2019

Abstract

Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.

Keywords

Acknowledgements

Acknowledgment

The authors thank John Galbraith, Lynda Khalaf, Hashem Pesaran, Giovanni Urga, Pascale Valéry, Victoria Zinde-Walsh, an anonymous referee, the Editor Justin Tobias, as well as several other seminar participants for useful comments. This work was supported by the William Dow Chair in Political Economy (McGill University), the Bank of Canada (Research Fellowship), the Toulouse School of Economics (Pierre-de-Fermat Chair of excellence), the Universitad Carlos III de Madrid (Banco Santander de Madrid Chair of excellence), a Guggenheim Fellowship, a Konrad-Adenauer Fellowship (Alexander-von-Humboldt Foundation, Germany), the Canadian Network of Centres of Excellence (program on Mathematics of Information Technology and Complex Systems (MITACS)), the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanities Research Council of Canada, and the Fonds de recherche sur la société et la culture (Québec).

Citation

Ahsan, M.N. and Dufour, J.-M. (2019), "A Simple Efficient Moment-based Estimator for the Stochastic Volatility Model", Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A (Advances in Econometrics, Vol. 40A), Emerald Publishing Limited, Bingley, pp. 157-201. https://doi.org/10.1108/S0731-90532019000040A008

Publisher

:

Emerald Publishing Limited

Copyright © 2019 Emerald Publishing Limited