On the criterion function for ARMA estimation
type: Item
instance of: scholarly article
title: On the criterion function for ARMA estimation
zbMATH Open document ID: 0787.62094
DOI: 10.1016/0378-3758(93)90141-R
published in: Journal of Statistical Planning and Inference
publication date: 1993-12-05T00:00:00Z
review text: It is shown that the asymptotic maximum-likelihood estimators for the parameters of stationary ARMA-models fulfill the conditions of stationarity and invertibility. For the criterion function of the conditional least-squares estimators, a matrix representation with lower- triangular Toeplitz matrices is given. Using circulant matrices a matrix representation is given of the frequency domain approximation of the likelihood function. It is shown that in this two cases the conditions of stationarity and invertibility are not always satisfied. Further some methods for reducing the bias of the estimators in the case of small samples are discussed.
reviewed by: G.Wittwer
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 445185
zbMATH Keywords: time series
zbMATH Keywords: small sample bias
zbMATH Keywords: bias reduction
zbMATH Keywords: asymptotic maximum- likelihood estimators
zbMATH Keywords: stationary ARMA-models
zbMATH Keywords: stationarity
zbMATH Keywords: invertibility
zbMATH Keywords: conditional least-squares estimators
zbMATH Keywords: matrix representation
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: circulant matrices
zbMATH Keywords: frequency domain approximation
author: D. Stephen G. Pollock
describes a project that uses: AS 175
MaRDI profile type: Publication
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full work available at URL: 0378-3758(93)90141-r
OpenAlex ID: W2100364250
description: scientific article; zbMATH DE number 445185