The relation of the CCA subspace method to a balanced reduction of an autoregressive model

In this paper we consider an identification procedure, called MEST, for multivariate time series based on AR-modeling and stochastically balanced truncation and compare it with the CCA subspace method. The stochastically balancing of multivariate AR-models is described using just linear algebraic operations, i.e., no algebraic Riccati equations need to be solved. Both identification procedures are formulated in a uniform manner, and from these expressions we conclude that the only difference is that MEST uses a covariance extension, whereas CCA is based on the sample covariances only. Finally, it is shown that MEST and CCA are asymptotically equivalent.