Discussion Paper Series 2009-E-23

Inconsistency of a Unit Root Test against Stochastic Unit Root Processes

Daisuke Nagakura

In this paper, 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 an 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

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

Copyright © 2009 Bank of Japan All Rights Reserved.

Home Japanese Home