  This paper extends the notion of information processing capacity for
non-independent input signals in the context of reservoir computing (RC). The
presence of input autocorrelation makes worthwhile the treatment of forecasting
and filtering problems for which we explicitly compute this generalized
capacity as a function of the reservoir parameter values using a streamlined
model. The reservoir model leading to these developments is used to show that,
whenever that approximation is valid, this computational paradigm satisfies the
so called separation and fading memory properties that are usually associated
with good information processing performances. We show that several standard
memory, forecasting, and filtering problems that appear in the parametric
stochastic time series context can be readily formulated and tackled via RC
which, as we show, significantly outperforms standard techniques in some
instances.
