Forecast density combinations with dynamic learning for large data sets in economics and finance

A flexible forecast density combination approach is introduced that can deal with large data sets. It extends the mixture of experts approach by allowing for model set incompleteness and dynamic learning of combination weights. A dimension reduction step is introduced using a sequential clustering mechanism that allocates the large set of forecast densities into a small number of subsets and the combination weights of the large set of densities are modelled as a dynamic factor model with a number of factors equal to the number of subsets. The forecast density combination is represented as a large finite mixture in nonlinear state space form. An efficient simulation-based Bayesian inferential procedure is proposed using parallel sequential clustering and filtering, implemented on graphics processing units. The approach is applied to track the Standard & Poor 500 index combining more than 7000 forecast densities based on 1856 US individual stocks that are are clustered in a relatively small subset. Substantial forecast and economic gains are obtained, in particular, in the tails using Value-at-Risk. Using a large macroeconomic data set of 142 series, similar forecast gains, including probabilities of recession, are obtained from multivariate forecast density combinations of US real GDP, Inflation, Treasury Bill yield and Employment. Evidence obtained on the dynamic patterns in the financial as well as macroeconomic clusters provide valuable signals useful for improved modelling and more effective economic and financial policies.