Modeling of perturbed covariance sequences

An algorithm for obtaining a state-space (Markovian) model of a random process from a finite number of estimated covariance lags is presented and compared to other SVD-based methods. The new algorithm performs well for small data sets in which the estimated covariance sequence is perturbed by estimation errors, and may not even be positive definite. Simulation results are presented for a second-order Markov process.