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Linear‐representation Based Estimation of Stochastic Volatility Models

Author

Listed:
  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris)

  • Jean‐michel Zakoïan

    (CREST - Centre de Recherche en Economie et Statistique [Bruz] - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique, IP Paris - Institut Polytechnique de Paris)

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," Post-Print hal-05431364, HAL.
    • Handle: RePEc:hal:journl:hal-05431364
    DOI: 10.1111/j.1467-9469.2006.00495.x
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