ABC-based forecasting in misspecified state space models

Approximate Bayesian Computation (ABC) has gained popularity as a method for conducting inference and forecasting in complex models, most notably those which are intractable in some sense. In this paper, we use ABC to produce probabilistic forecasts in state space models (SSMs). Whilst ABC-based forecasting in correctly-specified SSMs has been studied, the misspecified case has not been investigated. It is this case that we emphasize. We invoke recent principles of ‘focused’ Bayesian prediction, whereby Bayesian updates are driven by a scoring rule that rewards predictive accuracy; the aim being to produce predictives that perform well in that rule, despite misspecification. Two methods are investigated for producing the focused predictions. In a simulation setting, ‘coherent’ predictions are in evidence for both methods. That is, the predictive constructed using a particular scoring rule often predicts best according to that rule. Importantly, both focused methods typically produce more accurate forecasts than an exact but misspecified predictive, in particular when the degree of misspecification is marked. An empirical application to a truly intractable SSM completes the paper.