Inconsistency of a Unit Root Test against Stochastic Unit Root Processes
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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- Granger, Clive W. J. & Swanson, Norman R., 1997.
"An introduction to stochastic unit-root processes,"
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- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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