Asymptotic behaviour of the least squares estimator of the mean of AR(1) models
type: Item
instance of: scholarly article
title: Asymptotic behaviour of the least squares estimator of the mean of AR(1) models
zbMATH Open document ID: 1048.62081
DOI: 10.1023/B:ANAM.0000005368.92998.04
author: Yanyan Li
published in: Analysis Mathematica
publication date: 2004-10-19T00:00:00Z
review text: The shifted AR(1) model started at zero: \[ X_k^{(n)}=\alpha^{(n)}X_{k-1}^{(n)} + \varepsilon_k^{(n)},\;X_0^{(n)} =0,\;Z_k^{(n)}=X_k^{(n)} + m^{(n)}h\big(k/n\big),\quad k=1,2,\dots,\,n=1,2,\dots, \] where \(m^{(n)} \in R\) is an unknown parameter and \(h\) is a known real function, is considered. It is shown that the limit distribution of the MLS estimator of \(m^{(n)}\) based on \(\{Z_k^{(n)}: [T_1n] \leq k \leq [T_2n]\}\), where \(0 \leq T_1 <T_2\) is normal. The speed of convergence is different if \(n(1-\alpha^{(n)}) \to \gamma \in R\) or if \(n(1-\alpha^{(n)}) \to \pm \infty\). The stationary case of the shifted AR(1) model is also treated. Connection with the maximum likelihood estimator of the shift parameter of continuous AR(1) processes is discussed.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 2108654
zbMATH Keywords: nearly unstable
zbMATH Keywords: nearly stable
zbMATH Keywords: nearly explosive
zbMATH Keywords: AR(1) model
zbMATH Keywords: shift parameter
zbMATH Keywords: least squares estimator
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2108654