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Asymptotic Results for GMM Estimators of Stochastic Volatility Models

Author

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  • Geert Dhaene
  • Olivier Vergote

Abstract

We derive closed-form expressions for the optimal weighting matrix for GMM estimation of the stochastic volatility model with AR(1) log-volatility, and for the asymptotic covariance matrix of the resulting estimator. The moment conditions considered are generated by the absolute observations (which is the standard approach in this literature) or by the log-squared observations. We use the expressions to compare the performances of GMM and other estimators that have been proposed, and to optimally select small sets of moment conditions from very large sets.

Suggested Citation

  • Geert Dhaene & Olivier Vergote, 2003. "Asymptotic Results for GMM Estimators of Stochastic Volatility Models," Working Papers of Department of Economics, Leuven ces0306, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    • Handle: RePEc:ete:ceswps:ces0306
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    Cited by:

    1. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    2. Tsyplakov, Alexander, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models," MPRA Paper 25511, University Library of Munich, Germany.
    3. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Maddalena Cavicchioli, 2017. "Estimation and asymptotic covariance matrix for stochastic volatility models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 437-452, August.

    More about this item

    Keywords

    Stochastic volatility; GMM;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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