A Flexible Predictive Density Combination Model for Large Financial Data Sets in Regular and Crisis Periods

A flexible predictive density combination model is introduced for large financial data sets which allows for dynamic weight learning and model set incompleteness. Dimension reduction procedures allocate the large sets of predictive densities and combination weights to relatively small sets. Given the representation of the probability model in extended nonlinear state-space form, efficient simulation-based Bayesian inference is proposed using parallel sequential clustering as well as nonlinear filtering, implemented on graphics processing units. The approach is applied to combine predictive densities based on a large number of individual stock returns of daily observations over a period that includes the Covid-19 crisis period. Evidence on the quantification of predictive accuracy, uncertainty and risk, in particular, in the tails, may provide useful information for investment fund management. Information on dynamic cluster composition, weight patterns and model set incompleteness give also valuable signals for improved modelling and policy specification