Dynamic Predictive Density Combinations for Large Data Sets in Economics and Finance

markdownabstract__Abstract__ A Bayesian nonparametric predictive model is introduced to construct time-varying weighted combinations of a large set of predictive densities. A clustering mechanism allocates these densities into a smaller number of mutually exclusive subsets. Using properties of Aitchinson's geometry of the simplex, combination weights are defined with a probabilistic interpretation. The class-preserving property of the logistic-normal distribution is used to define a compositional dynamic factor model for the weight dynamics with latent factors defined on a reduced dimension simplex. Groups of predictive models with combination weights are updated with parallel clustering and sequential Monte Carlo filters. The procedure is applied to predict Standard & Poor's 500 index using more than 7000 predictive densities based on US individual stocks and finds substantial forecast and econ omic gains. Similar forecast gains are obtained in point and density forecasting of US real GDP, Inflation, Treasury Bill yield and employment using a large data set