  Nonlinear stochastic modeling is useful for describing complex engineering
systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are
developing to tackle tasks that are challenging and resource intensive on
digital computers. An emerging scheme is reservoir computing which exploits
nonlinear dynamical systems for temporal information processing. This paper
introduces reservoir computers with output feedback as stationary and ergodic
infinite-order nonlinear autoregressive models. We highlight the versatility of
this approach by employing classical and quantum reservoir computers to model
synthetic and real data sets, further exploring their potential for control
applications.
