State space modeling of time series
State space modeling of time series
The statistical theory of linear systems
The statistical theory of linear systems
On the L∞ consistency of L2 estimators
Systems & Control Letters
A tighter relative-error bound for balanced stochastic truncation
Systems & Control Letters
The distribution of zeros of asymptotically extremal polynomials
Journal of Approximation Theory
Digital processing of random signals: theory and methods
Digital processing of random signals: theory and methods
On the Nonlinear Dynamics of Fast Filtering Algorithms
SIAM Journal on Control and Optimization
Automatica (Journal of IFAC)
Experimental evidence showing that stochastic subspace identification methods may fail
Systems & Control Letters
A Convex Optimization Approach to the Rational Covariance Extension Problem
SIAM Journal on Control and Optimization
Brief papers: Linear identification of ARMA processes
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
In this paper we consider a three-step procedure for identification of time series, based on covariance extension and model reduction, and we present a complete analysis of its statistical convergence properties. A partial covariance sequence is estimated from statistical data. Then a high-order maximum-entropy model is determined, which is finally approximated by a lower-order model by stochastically balanced model reduction. Such procedures have been studied before, in various combinations, but an overall convergence analysis comprising all three steps has been lacking. Supposing the data is generated from a true finite-dimensional system which is minimum phase, it is shown that the transfer function of the estimated system tends in H^~ to the true transfer function as the data length tends to infinity, if the covariance extension and the model reduction is done properly. The proposed identification procedure, and some variations of it, are evaluated by simulations.