Limiting power of unit-root tests in time-series regression
type: Item
instance of: scholarly article
title: Limiting power of unit-root tests in time-series regression
zbMATH Open document ID: 0722.62057
DOI: 10.1016/0304-4076(90)90010-Q
author: Seiji Nabeya
author: Katsuto Tanaka
published in: Journal of Econometrics
publication date: 1990-01-01T00:00:00Z
review text: The model considered in this paper is \(y_ t=x'_ t\beta +\eta_ t\), \(\eta_ t=\rho \eta_{t-1}+v_ t\), where \(y_ t\) is scalar, \(x_ t\) is a nonstochastic vector, and the \(v_ t\) are martingale differences satisfying certain moment conditions. To test \(H_ 0: \rho =1\) against \(H_ 1: \rho <1\) or \(H'_ 1: \rho >1\), six different test statistics are considered, all defined as ratios of quadratic forms in \({\hat \eta}{}_ t's\) (residuals from ordinary least squares estimation), or \({\tilde \eta}{}_ t's\) (residuals from generalized least squares estimation). Local alternatives with \(\rho =1-c/T\) (c a constant, T sample size) are studied. The authors conclude that ``the limiting powers of some unit- root tests are computed accurately under a sequence of local alternatives. The limiting powers are found to give a good approximation to the finite-sample powers. An extension of the model is also discussed allowing for autocorrelated errors in the AR(1) process''.
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 4190957
zbMATH Keywords: time-series regression
zbMATH Keywords: martingale differences
zbMATH Keywords: ratios of quadratic forms
zbMATH Keywords: residuals from ordinary least squares estimation
zbMATH Keywords: residuals from generalized least squares estimation
zbMATH Keywords: limiting powers
zbMATH Keywords: unit-root tests
zbMATH Keywords: sequence of local alternatives
zbMATH Keywords: autocorrelated errors
zbMATH Keywords: AR(1) process
MaRDI profile type: Publication
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full work available at URL: 0304-4076(90)90010-q
OpenAlex ID: W2084881743
description: scientific article; zbMATH DE number 4190957