Estimation of parameters and eigenmodes of multivariate autoregressive models

Citation
A. Neumaier et T. Schneider, Estimation of parameters and eigenmodes of multivariate autoregressive models, ACM T MATH, 27(1), 2001, pp. 27-57
Citations number
27
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Science & Engineering
Journal title
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
ISSN journal
0098-3500 → ACNP
Volume
27
Issue
1
Year of publication
2001
Pages
27 - 57
Database
ISI
SICI code
0098-3500(200103)27:1<27:EOPAEO>2.0.ZU;2-U
Abstract
Dynamical characteristics of a complex system can often be inferred from an alyses of a stochastic time series model fitted to observations of the syst em. Oscillations in geophysical systems, for example, are sometimes charact erized by principal oscillation patterns, eigenmodes of estimated autoregre ssive (AR) models of first order. This paper describes the estimation of ei genmodes of AR models of arbitrary order. AR processes of any order can be decomposed into eigenmodes with characteristic oscillation periods, damping times, and excitations. Estimated eigenmodes and confidence intervals for the eigenmodes and their oscillation periods and damping times can be compu ted from estimated model parameters. As a computationally efficient method of estimating the parameters of AR models from high-dimensional data, a ste pwise least squares algorithm is proposed. This algorithm computes model co efficients and evaluates criteria for the selection of the model order step wise for AR models of successively decreasing order. Numerical simulations indicate that, with the least squares algorithm, the AR model coefficients and the eigenmodes derived from the coefficients are estimated reliably and that the approximate 95% confidence intervals for the coefficients and eig enmodes are rough approximations of the confidence intervals inferred from the simulations.