  Building upon the pertinence of the factor decomposition to break the curse
of dimensionality inherent to multivariate volatility processes, we develop a
factor model-based multivariate stochastic volatility (fMSV) framework that
relies on two viewpoints: sparse approximate factor model and sparse factor
loading matrix. We propose a two-stage estimation procedure for the fMSV model:
the first stage obtains the estimators of the factor model, and the second
stage estimates the MSV part using the estimated common factor variables. We
derive the asymptotic properties of the estimators. Simulated experiments are
performed to assess the forecasting performances of the covariance matrices.
The empirical analysis based on vectors of asset returns illustrates that the
forecasting performances of the fMSV models outperforms competing conditional
covariance models.
