  Approximate Bayesian Computation (ABC) has become increasingly prominent as a
method for conducting parameter inference in a range of challenging statistical
problems, most notably those characterized by an intractable likelihood
function. In this paper, we focus on the use of ABC not as a tool for
parametric inference, but as a means of generating probabilistic forecasts; or
for conducting what we refer to as `approximate Bayesian forecasting'. The four
key issues explored are: i) the link between the theoretical behavior of the
ABC posterior and that of the ABC-based predictive; ii) the use of proper
scoring rules to measure the (potential) loss of forecast accuracy when using
an approximate rather than an exact predictive; iii) the performance of
approximate Bayesian forecasting in state space models; and iv) the use of
forecasting criteria to inform the selection of ABC summaries in empirical
settings. The primary finding of the paper is that ABC can provide a
computationally efficient means of generating probabilistic forecasts that are
nearly identical to those produced by the exact predictive, and in a fraction
of the time required to produce predictions via an exact method. y identical to
those produced by the exact predictive, and in a fraction of the time required
to produce predictions via an exact method.
