A finite-interval stochastically balanced realization is analyzed based on the idealized assumption that an exact finite covariance sequence is available. It is proved that a finite-interval balanced realization algorithm [Maciejowski, J. M. (1996). Parameter estimation of multivariable systems using balanced realizations. In S. Bittanti, & G. Picci (Eds.), Identification, adaptation, learning (pp. 70-119). Berlin: Springer] provides stable minimum phase models, if the size of the interval is at least two times larger than the order of a minimal realization. New algorithms for finite-interval stochastic realization and stochastic subspace identification are moreover derived by means of block LQ decomposition, and the stability and minimum phase properties of models obtained by these algorithms are considered. Numerical simulation results are also included. (C) 2007 Elsevier Ltd. All rights reserved.