Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship

Frédérique Bec · Mélika Ben Salem · Marine Carrasco

141 citations0/0 files storedJournal of Business and Economic Statistics

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Monetary Policy and Economic Impact Global Financial Crisis and Policies Diverse Scientific and Economic Studies

Abstract

We consider modeling the real exchange rate by a stationary three-regime self-exciting threshold autoregressive (SETAR) model with possibly a unit root in the middle regime. This representation is consistent with purchasing power parity in the presence of trading costs. Our main contribution is to provide statistical tools for testing unit root versus a SETAR. First, we show that a SETAR with a unit root in the middle regime is stationary and mixing under reasonable assumptions. Second, we derive analytically the asymptotic distribution of our unit-root test under the null. Using monthly real exchange rate data, our test rejects the null of unit-root against a threshold process for five European series.

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References

1988Testing for a Unit Root in Time Series Regression 1981Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root 1992Testing the null hypothesis of stationarity against the alternative of a unit root 1964The Purchasing-Power Parity Doctrine: A Reappraisal 1997Foundations of International Macroeconomics 1996The Purchasing Power Parity Puzzle 1964Theoretical Notes on Trade Problems 1996Inference When a Nuisance Parameter Is Not Identified Under the Null Hypothesis

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