  Inference and forecast problems of the nonlinear dynamical system have arisen
in a variety of contexts. Reservoir computing and deep sequential models, on
the one hand, have demonstrated efficient, robust, and superior performance in
modeling simple and chaotic dynamical systems. However, their innate
deterministic feature has partially detracted their robustness to noisy system,
and their inability to offer uncertainty measurement has also been an
insufficiency of the framework. On the other hand, the traditional state-space
model framework is robust to noise. It also carries measured uncertainty,
forming a just-right complement to the reservoir computing and deep sequential
model framework. We propose the unscented reservoir smoother, a model that
unifies both deep sequential and state-space models to achieve both frameworks'
superiorities. Evaluated in the option pricing setting on top of noisy
datasets, URS strikes highly competitive forecasting accuracy, especially those
of longer-term, and uncertainty measurement. Further extensions and
implications on URS are also discussed to generalize a full integration of both
frameworks.
