Identification of nonstationary multivariate autoregressive processes - Comparison of competitive and collaborative strategies for joint selection of estimation bandwidth and model order

The problem of identification of multivariate autoregressive processes (systems or signals) with unknown and possibly time-varying model order and time-varying rate of parameter variation is considered and solved using parallel estimation approach. Under this approach, several local estimation algorithms, with different order and bandwidth settings, are run simultaneously and compared based on their predictive performance. First, the competitive decision schemes are considered. It is shown that the best parameter tracking results can be obtained when the order is selected based on minimization of the appropriately modified Akaike's final prediction error statistic, and the bandwidth is chosen using the localized version of the Rissanen's predictive least squares statistic. Next, it is shown that estimation results can be further improved if a collaborative decision is made by means of applying the Bayesian model averaging technique.