Abstract
We propose a new approach to performing Bayesian forecasting in state space models that yields accurate predictions without relying on correct model specification. This new approach constructs a predictive distribution using approximate Bayesian computation (ABC). The summary statistics that underpin ABC are produced via a criterion function that rewards a user-specified measure of predictive accuracy and, in so doing, produces a predictive distribution that performs well in that measure. The method is illustrated numerically using simulated data, demonstrating its effectiveness, including in comparison with exact MCMC-based predictions. In particular, coherent predictions are in evidence, whereby the ABC predictive constructed via the use of a particular scoring rule, is shown to perform the best out of sample according to that rule, and better than the exact (but misspecified) Bayesian predictive.