  Filtering has had a profound impact as a device of perceiving information and
deriving agent expectations in dynamic economic models. For an abstract
economic system, this paper shows that the foundation of applying the filtering
method corresponds to the existence of a conditional expectation as an
equilibrium process. Agent-based rational behavior of looking backward and
looking forward is generalized to a conditional expectation process where the
economic system is approximated by a class of models, which can be represented
and estimated without information loss. The proposed framework elucidates the
range of applications of a general filtering device and is not limited to a
particular model class such as rational expectations.

Probability