  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, and it is that case which 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:
the predictive constructed via the use of a particular scoring rule predicts
best according to that rule. Importantly, both focused methods typically
produce more accurate forecasts than an exact, but misspecified, predictive. An
empirical application to a truly intractable SSM completes the paper.
