DMCA
Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models (2001)
Cached
Download Links
| Citations: | 103 - 2 self |
BibTeX
@MISC{Neumaier01estimationof,
author = {Arnold Neumaier and Tapio Schneider},
title = {Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models},
year = {2001}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Dynamical characteristics of a complex system can often be inferred from analyses of a stochastic time series model fitted to observations of the system. Oscillations in geophysical systems, for example, are sometimes characterized by principal oscillation patterns, eigenmodes of estimated autoregressive (AR) models of first order. This paper describes the estimation of eigenmodes 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 computed from estimated model parameters. As a computationally efficient method of estimating the parameters of AR models from high-dimensional data, a stepwise least squares algorithm is proposed. This algorithm computes model coefficients and evaluates criteria for the selection of the model order stepwise 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 eigenmodes are rough approximations of the confidence intervals inferred from the simulations.
Keyphrases
ar model multivariate autoregressive model confidence interval stochastic time series model oscillation period rough approximation high-dimensional data complex system ar process first order principal oscillation pattern geophysical system efficient method model parameter stepwise least square arbitrary order model coefficient numerical simulation characteristic oscillation period dynamical characteristic ar model coefficient model order stepwise
