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Estimating high dimensional multivariate stochastic volatility models

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  • Matteo Pelagatti
  • Giacomo Sbrana

Abstract

This paper proposes tree main results that enable the estimation of high dimensional multivariate stochastic volatility models. The first result is the closed-form steady-state Kalman filter for the multivariate AR(1) plus noise model. The second result is an accelerated EM algorithm for parameters estimation. The third result is an estimator of the correlation of two elliptical random variables with time-varying variances that is consistent and asymptotically normal regardless of the variances evolution. Speed and precision of our methodology are evaluated in a simulation experiment. Finally, we implement our method and compare its performance with other approaches in a minimum variance portfolio composed by the constituents of the CAC40 and S&P100 indexes.

Suggested Citation

  • Matteo Pelagatti & Giacomo Sbrana, 2020. "Estimating high dimensional multivariate stochastic volatility models," Working Papers 428, University of Milano-Bicocca, Department of Economics, revised Jan 2020.
    • Handle: RePEc:mib:wpaper:428
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    References listed on IDEAS

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    Keywords

    Riccati equation; EM algorithm; Kalman filter; Correlation estimation; Large covariance matrix; Multivariate stochastic volatility;
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