Stationarity conditions for linear models

AbstractThe problem of building a linear stationary model for a process given by evenly spaced discrete or continuous observations is considered. Criteria are proposed for the existence of such a model governed by a vector difference or differential equation. Various model representations in discrete and continuous forms are studied and numerical methods for their identification are developed. This gives the order and dynamics of a model in the canonical form. To include processes in noisy environment, a moving average of observations is introduced into deterministic identification algorithms. Different integral forms of the moving average of continuous observations are proposed for identification of models governed by a system of linear stationary differential equations. Discussion of some experimental and computational results is presented