On Building Nonlinear Dynamical Stochastic Process Models from Empirical Data

Attention is then directed toward using a construction due to Wiener and Nisio, built upon a typical path of the process data, which could serve as a starting cadidate white noise functional. The given scalar process must be stationalary, ergodic, and continuous in probability. The sequence of Wiener-Nisio functionals, when driven by the flow of the white noise excitation gives rise to output processes which converge in finite-order distributions to the given process. The functional admits a causal Wiener series expansion which, when truncated, is realizable as a finite-order causal bilinear dynamical system driven by white noise excitation which also approximates the given process in finite distributions.