Linear system identification from non-stationary cross-sectional data

The identification of time invariant linear stochastic systems from cross-sectional data on non-stationary system behavior is considered. A strong consistency and asymptotic normality result for maximum likelihood and prediction error estimates of the system parameters, system and measurement noise covariances and the initial state covariance is proven. A new identifiability property for the system model is defined and appears in the set of conditions for this result. The non-stationary stochastic realization (i.e., covariance factorization) theorem in [1] describes sufficient conditions for the identifiability property to hold. An application illustrating the use of a computer program implementing the identification method is presented.