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This paper extends the notion of information processing capacity fornon-independent input signals in the context of reservoir computing (RC). Thepresence of input autocorrelation makes worthwhile the treatment of forecastingand filtering problems for which we explicitly compute this generalizedcapacity as a function of the reservoir parameter values using a streamlinedmodel. The reservoir model leading to these developments is used to show that,whenever that approximation is valid, this computational paradigm satisfies theso called separation and fading memory properties that are usually associatedwith good information processing performances. We show that several standardmemory, forecasting, and filtering problems that appear in the parametricstochastic time series context can be readily formulated and tackled via RCwhich, as we show, significantly outperforms standard techniques in someinstances.

Quantitative evaluation of the performance of discrete-time reservoir  computers in the forecasting, filtering, and reconstruction of stochastic  stationary signals