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Linear‐representation Based Estimation of Stochastic Volatility Models

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  • CHRISTIAN FRANCQ
  • JEAN‐MICHEL ZAKOÏAN

Abstract

. A new way of estimating stochastic volatility models is developed. The method is based on the existence of autoregressive moving average (ARMA) representations for powers of the log‐squared observations. These representations allow to build a criterion obtained by weighting the sums of squared innovations corresponding to the different ARMA models. The estimator obtained by minimizing the criterion with respect to the parameters of interest is shown to be consistent and asymptotically normal. Monte‐Carlo experiments illustrate the finite sample properties of the estimator. The method has potential applications to other non‐linear time‐series models.

Suggested Citation

  • Christian Francq & Jean‐Michel Zakoïan, 2006. "Linear‐representation Based Estimation of Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 785-806, December.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:4:p:785-806
    DOI: 10.1111/j.1467-9469.2006.00495.x
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    1. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
    2. Breitung, Jörg & Hafner, Christian M., 2016. "A simple model for now-casting volatility series," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1247-1255.
    3. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    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.
    5. Ahsan, Md. Nazmul & Dufour, Jean-Marie, 2021. "Simple estimators and inference for higher-order stochastic volatility models," Journal of Econometrics, Elsevier, vol. 224(1), pages 181-197.
    6. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.
    7. Sucarrat, Genaro, 2010. "The power log-GARCH model," UC3M Working papers. Economics we1013, Universidad Carlos III de Madrid. Departamento de Economía.

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