Estimating the dimension of a linear system

DOI10.1016/0047-259X(81)90089-0zbMath0501.93065MaRDI QIDQ1172612

E. J. Hannan

Publication date: 1981

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

iterated logarithmweak and strong convergencelinear stochastic systemMcMillan degreeKronecker indicesergodic stationary process

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Estimation and detection in stochastic control theory (93E10) Identification in stochastic control theory (93E12) Inference from stochastic processes (62M99)

Related Items (12)

Twenty-one ML estimators for model selection ⋮ Inferring the rank of a matrix ⋮ ESTIMATION OF AUTOREGRESSIVE MOVING-AVERAGE ORDER GIVEN AN INFINITE NUMBER OF MODELS AND APPROXIMATION OF SPECTRAL DENSITIES ⋮ Differential geometry of a parametric family of invertible linear systems—Riemannian metric, dual affine connections, and divergence ⋮ Order Choice in Nonlinear Autoregressive Models ⋮ Extimation and structure determination of multivariate input systems ⋮ Some properties of the parameterization of ARMA systems with unknown order ⋮ Strong consistency of a family of model order selection rules for estimating 2D sinusoids in noise ⋮ ON THE RECURSIVE FITTING OF SUBSET AUTOREGRESSIONS ⋮ On the underfitting and overfitting sets of models chosen by order selection criteria. ⋮ Consistency of a class of information criteria for model selection in non-linear regression ⋮ Multivariate subset autoregressive modelling with zero constraints for detecting 'overall causality'

Cites Work

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• Estimation of vector Armax models
• The estimation of the order of an ARMA process
• Some properties of the parameterization of ARMA systems with unknown order
• Fitting autoregressive models for prediction
• Canonical forms for the identification of multivariable linear systems
• Vector linear time series models
• Selection of the order of an autoregressive model by Akaike's information criterion
• Vector linear time series models: corrections and extensions
• Consistent estimation of system order
• The Representation of Functionals of Brownian Motion by Stochastic Integrals
• Asymptotic Independence of the Numbers of High and Low Level Crossings of Stationary Gaussian Processes

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