Latent factor models with conditional heteroskedasticity: estimation and forecast

A large latent factor model, in which the volatilities of common and idiosyncratic factors are conditionally heteroskedastic, is considered. Exact likelihood-based estimation methods are not available when conditional variances depend on past values of the latent factors (common or specific). Indirect estimation procedures are available in the literature. Some of them calibrate the score of a Kalman filter approximation with inequality constraints on the auxiliary model parameters. Others deal sequentially with univariate linear regressions and univariate Garch-type models; they proved to be almost as accurate as the previous, with a remarkable computational simplification and speed. Volatility forecasts require the application of a Metropolis algorithm. This can also be done with two different approaches. (1) Multiple-move approach, simpler and faster, with the possible disadvantage of higher rejection probability even with a good proposal distribution. (2) Single-move approach, more complicated and computationally slower, with the possible advantage of a higher efficiency (in statistical terms) due to a very low rejection probability. We fully discuss computational details of the methods and we report the results of an extensive Monte Carlo experiment with empirically realistic designs to evaluate the performance of estimators and forecasts. Finally, we present an application on a moderately large number of weekly and daily returns from the stock market.