A solution to the problem of constructing a state space model from time series

The problem of constructing minimal realizations from arbitrary input-output time series which are only covariance stationary (not necessarily stationary) is considered. An algorithm which solves this problem for a fairly nonrestrictive class of exogenous (input) signals is presented. The algorithm is based upon modeling nonzero exogenous signals by linear models and including these in the total system model.<>