Optimization and Systems Theory
A class of methods called subspace methods has attracted a lot of attention due to their advantages in modeling time series and especially multivariate time series. However, these methods are based on an unnatural assumption and therefore an alternative identification procedure is presented. It is based on identification of a high-order Maximum Entropy model (AR model) followed by Stochastically balanced Truncation (MEST). The MEST procedure is described using just linear algebraic operations, and therefore it inherits the nice properties of subspace methods. Actually, MEST is very closely related to the subspace methods. The essential differences between the CCA subspace method of Larimore and MEST are: CCA estimates all covariances in a block Hankel matrix directly from data, whereas MEST uses covariance extension when constructing the Hankel matrix. By increasing the AR-model order in a proper manner, strong consistency and asymptotic normality of MEST is obtained. In fact, MEST and the CCA subspace method are asymptotically equivalent, which implies that they have the same asymptotic normal distribution. However, simulations indicate that MEST has a better performance than CCA in practice.