  In the following article we consider approximate Bayesian computation (ABC)
for certain classes of time series models. In particular, we focus upon
scenarios where the likelihoods of the observations and parameter are
intractable, by which we mean that one cannot evaluate the likelihood even
up-to a positive unbiased estimate. This paper reviews and develops a class of
approximation procedures based upon the idea of ABC, but, specifically
maintains the probabilistic structure of the original statistical model. This
idea is useful, in that it can facilitate an analysis of the bias of the
approximation and the adaptation of established computational methods for
parameter inference. Several existing results in the literature are surveyed
and novel developments with regards to computation are given.
