Validation of State Space Models in Non-Gaussian Systems

A methodology for testing whether a state space model accurately describes the system under consideration is presented. Unlike existing procedures it is not necessary to assume that all of the random terms in the model are normally distributed. The methodology is based on a single realization of observations and is relatively easy to implement since it is based on a normalized Kalman filter state estimate. The testing procedure rests on an asymptotic distribution theory for the filter estimate. The power of the methodology to detect modeling errors varies considerably according to the type of error occurring.