A Bayesian Dynamic Compositional Model for Large Density Combinations in Finance

A Bayesian dynamic compositional model is introduced that can deal with combining a large set of predictive densities. It extends the mixture of experts and the smoothly mixing regression models by allowing for combination weight dependence across models and time. A compositional model with Logistic-normal noise is specified for the latent weight dynamics and the class-preserving property of the logistic-normal is used to reduce the dimension of the latent space and to build a compositional factor model. The projection used in the dimensionality reduction is based on a dynamic clustering process which partitions the large set of predictive densities into a smaller number of subsets. We exploit the state space form of the model to provide an efficient inference procedure based on Particle MCMC. The approach is applied to track the Standard \& Poor 500 index combining 3712 predictive densities, based on 1856 US individual stocks, clustered in relatively small number of model sets. For the period 2007-2009, which included the financial crisis, substantial predictive gains are obtained, in particular, in the tails using Value-at-Risk. Similar predictive gains are obtained for the US Treasury Bill yield using a large set of macroeconomic variables. Evidence obtained on model set incompleteness and dynamic patterns in the financial clusters provide valuable signals for improved modelling and more effective economic and financial decisions.