Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process

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4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2476-2483
Number of pages8
JournalStatistics and Probability Letters
Volume79
Issue number24
DOIs
Publication statusPublished - 2009 Dec 15
Externally publishedYes

Fingerprint

Random Coefficient Models
Unit Root Tests
Unit Root
Asymptotic Theory
Autoregressive Model
Inconsistency
Locally Best Invariant Test
Dickey-Fuller Test
Inconsistent
Null
Class
Random coefficients
Asymptotic theory
Autoregressive model
Stochastic unit roots
Unit root tests
Alternatives

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

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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.",
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AB - 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.

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