ABSTRACT
This chapter describes a technique for nonlinear system identification that is based on prediction error minimization. Generalizability is achieved when the current parameter estimates suffice to predict future time series generated by the same information processing system from which the parameters were originally estimated. The Kronecker product vector is related to the convolution vector used in communications theory and in the theory of distributed associative memory model (TODAM) for human memory. The transfer function matrices might represent the stored spatiotemporal knowledge required to perform a psychomotor skill, such as playing the piano, using a computer keyboard, or handwriting. According to Chen, Billings and Grant, the standard method for modeling nonlinear time series, especially in economics, is the nonlinear autoregressive moving average with exogenous inputs (NARMAX) model. The gradient-descent error minimization version of the nonlinear system identification model provides an adequate fit to empirical time series data obtained in a variety of experimental contexts.
