Before revision:  A two-stage dynamic factor model method recovering  common and idiosyncratic volatility shocks therefore was proposed in Barigozzi and Hallin (2016).
After revision:  A two-stage dynamic factor model method recovering common and idiosyncratic components of both levels and log-volatilities. Specifically, in a first estimation step, we extract the common and idiosyncratic shocks for the levels, from which a log-volatility proxy is computed. In a second step, we estimate a dynamic factor model, which is equivalent to a multiplicative factor structure for volatilities, for the log-volatility panel.