  Following the idea of Bayesian learning via Gaussian mixture model, we
organically combine the backward-looking information contained in the
historical data and the forward-looking information implied by the market
portfolio, which is affected by heterogeneous expectations and noisy trading
behavior. The proposed combined estimation adaptively harmonizes these two
types of information based on the degree of market efficiency and responds
quickly at turning points of the market. Both simulation experiments and a
global empirical test confirm that the approach is a flexible and robust
forecasting tool and is applicable to various capital markets with different
degrees of efficiency.
