Identification of echelon canonical forms for vector linear processes using least squares
type: Item
instance of: scholarly article
title: Identification of echelon canonical forms for vector linear processes using least squares
zbMATH Open document ID: 0756.62033
author: D. S. Poskitt
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: To identify stationary and invertible \(p\)-dimensional autoregressive- moving-average (ARMA) processes, the author considers models that are presumed to be represented in (reversed) echelon canonical form. The least squares method is used to estimate the model parameters. When the transfer function of the process is assumed to be rational and the model structure is given, the consistency of the least squares estimator is shown (theorem 3.1 and corollary 3.1). In section 4, a consistency procedure is presented to determine a (reversed) echelon canonical form structure (theorem 4.1). In section 5, when the transfer function of the process is nonrational, under little modifications of the assumptions on the model assumed above, the consistency of the least squares estimator still holds (but with a slower speed of convergence), and the result to determine the model structure remains true.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 93E12
zbMATH DE Number: 61835
zbMATH Keywords: stationary, invertible vector autoregressive moving-average time series
zbMATH Keywords: determination of structural indices
zbMATH Keywords: closed form least squares calculations
zbMATH Keywords: Kronecker indices
zbMATH Keywords: identification
zbMATH Keywords: least squares regression
zbMATH Keywords: echelon canonical form
zbMATH Keywords: transfer function
zbMATH Keywords: consistency
zbMATH Keywords: speed of convergence
reviewed by: Mohamed Boutahar
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348518
OpenAlex ID: W2089155713
DOI: 10.1214/AOS/1176348518
description: scientific article; zbMATH DE number 61835