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UNIT ROOT TEST IN A THRESHOLD AUTOREGRESSION: ASYMPTOTIC THEORY AND RESIDUAL-BASED BLOCK BOOTSTRAP

Published online by Cambridge University Press:  17 July 2008

Myung Hwan Seo
Myung Hwan Seo*
Affiliation:
London School of Economics
*
Address correspondence to Myung Hwan Seo, Department of Economics, London School of Economics, Houghton Street, London, WC2A 2AE, United Kingdom; e-mail: m.seo@lse.ac.uk
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Abstract

This paper develops a test of the unit root null hypothesis against a stationary threshold process. This testing problem is nonstandard and complicated because a parameter is unidentified and the process is nonstationary under the null hypothesis. We derive an asymptotic distribution for the test, which is not pivotal without simplifying assumptions. A residual-based block bootstrap is proposed to calculate the asymptotic p-values. The asymptotic validity of the bootstrap is established, and a set of Monte Carlo simulations demonstrates its finite-sample performance. In particular, the test exhibits considerable power gains over the augmented Dickey–Fuller (ADF) test, which neglects threshold effects.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 6 , December 2008 , pp. 1699 - 1716
Copyright
Copyright © Cambridge University Press 2008

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