Inconsistency of a Unit Root Test Against a Stochastic Unit Root Process

11 Pages Posted: 12 Nov 2008 Last revised: 26 Jun 2017

See all articles by Daisuke Nagakura

Daisuke Nagakura

Keio University - Faculty of Economics

Date Written: November 12, 2008

Abstract

In this article, we develop the asymptotic theory of Hwang and Basawa (2005) for explosive random coefficient autoregressive (ERCA) models. Applying the theory, we prove that a locally best invariant (LBI) test in McCabe and Tremayne (1995), which is for the null of a unit root (UR) process against the alternative of a stochastic unit root (STUR) process, is inconsistent against a class of ERCA models. This class includes a class of STUR processes as special cases. We show, however, that the well-known Dickey-Fuller(DF) UR tests and a LBI test of Lee (1998) are consistent against a particular case of this class of ERCA models.

Keywords: locally best invariant test, consistency, Dickey Fuller test, LBI, RCA, STUR

JEL Classification: C12

Suggested Citation

Nagakura, Daisuke, Inconsistency of a Unit Root Test Against a Stochastic Unit Root Process (November 12, 2008). Available at SSRN: https://ssrn.com/abstract=1300074 or http://dx.doi.org/10.2139/ssrn.1300074

Daisuke Nagakura (Contact Author)

Keio University - Faculty of Economics ( email )

2-15-45 Mita, Ninato-ku
Tokyo 1088345
Japan

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