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STATISTICS & PROBABILITY LETTERS
Volume 79, Issue 24, Pages 2476-2483Publisher
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DOI: 10.1016/j.spl.2009.09.001
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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. (C) 2009 Elsevier B.V. All rights reserved.
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