Structure and order estimation of multivariable stochastic processes

This note presents a procedure allowing us to estimate the structure of a state-space representation for a multivariable stationary stochastic process from measured output data. It is assumed that the observed vector time series is a realization of a process with rational spectrum or the output of a stable, time-invariant, linear system driven by white noise. The paper proposes an algorithm which selects a maximal set of linearly independent rows of the Hankel matrix built upon the estimated covariance sequence and which thus yields estimates of the Kronecker invariants.