Nonlinear mean-reversion to purchasing power parity: exponential smooth transition autoregressive models and stochastic unit root processes

Abstract

Nonlinear exponential smooth transition autoregressive (ESTAR) models are recently very popular in modelling the deviation from purchasing power parity. This article, shows that there is a close relation between the ESTAR models estimated in Taylor et al. (2001 Taylor, MP, Peel, DA and Sarno, L. 2001. Nonlinear mean-reversion in real exchange rates: toward a solution to the purchasing power parity puzzles. International Economic Review, 42: 1015–42. [Crossref], [Web of Science ®] , [Google Scholar]) and stochastic unit root (STUR) processes of Granger and Swanson (1997 Granger, CWJ and Swanson, NR. 1997. An introduction to stochastic unit-root processes. Journal of Econometrics, 80: 35–62. [Crossref], [Web of Science ®] , [Google Scholar]) and McCabe and Tremayne (1995 McCabe, BPM and Tremayne, AR. 1995. Testing a time series for difference stationarity. Annals of Statistics, 23: 1015–28. [Crossref], [Web of Science ®] , [Google Scholar]). Also, for a post-Bretton Woods sample period, the real exchange rates from four major countries are tested if they are better described as I(1), ESTAR or STUR processes.

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