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Inconsistency of a Unit Root Test against Stochastic Unit Root Processes

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  • Daisuke Nagakura

    (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: daisuke.nagakura@boj.or.jp))

Abstract

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.

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Bibliographic Info

Paper provided by Institute for Monetary and Economic Studies, Bank of Japan in its series IMES Discussion Paper Series with number 09-E-23.

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Date of creation: Oct 2009
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Handle: RePEc:ime:imedps:09-e-23

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Related research

Keywords: Locally Best Invariant Test; Consistency; Dickey-Fuller Test; LBI; RCA; STUR;

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  1. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, 07.
  2. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  3. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
  4. Michael Bleaney & Stephen J. Leybourne, 2003. "Real Exchange Rate Dynamics Under The Current Float: A Re-Examination," Manchester School, University of Manchester, vol. 71(2), pages 156-171, 03.
  5. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, 01.
  6. Daisuke Nagakura, 2007. "Testing for Coefficient Stability of AR(1) Model When the Null is an Integrated or a Stationary Process," IMES Discussion Paper Series 07-E-20, Institute for Monetary and Economic Studies, Bank of Japan.
  7. Michael F. Bleaney & Stephen J. Leybourne & Paul Mizen, 1999. "Mean Reversion of Real Exchange Rates in High-Inflation Countries," Southern Economic Journal, Southern Economic Association, vol. 65(4), pages 839-854, April.
  8. Robert Sollis & Paul Newbold & Stephen Leybourne, 2000. "Stochastic unit roots modelling of stock price indices," Applied Financial Economics, Taylor & Francis Journals, vol. 10(3), pages 311-315.
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