This paper develops an asymptotic theory of inference for an unrestricted two-regime threshold autoregressive (TAR) model with an autoregressive unit root. We find that the asymptotic null distribution of Wald tests for a threshold are nonstandard and different from the stationary case, and suggest basing inference on a bootstrap approximation. We also study the asymptotic null distributions of tests for an autoregressive unit root, and find that they are nonstandard and dependent on the presence of a threshold effect. We propose both asymptotic and bootstrap-based tests. These tests and distribution theory allow for the joint consideration of nonlinearity (thresholds) and nonstationary (unit roots). Our limit theory is based on a new set of tools that combine unit root asymptotics with empirical process methods. We work with a particular two-parameter empirical process that converges weakly to a two-parameter Brownian motion. Our limit distributions involve stochastic integrals with respect to this two-parameter process. This theory is entirely new and may find applications in other contexts. We illustrate the methods with an application to the U.S. monthly unemployment rate. We find strong evidence of a threshold effect. The point estimates suggest that the threshold effect is in the short-run dynamics, rather than in the dominate root. While the conventional ADF test for a unit root is insignificant, our TAR unit root tests are arguably significant. The evidence is quite strong that the unemployment rate is not a unit root process, and there is considerable evidence that the series is a stationary TAR process. Copyright The Econometric Society.
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Article provided by Econometric Society in its journal Econometrica.
Volume (Year): 69 (2001) Issue (Month): 6 (November) Pages: 1555-1596 Download reference. The following formats are available: HTML
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Balke, Nathan S & Fomby, Thomas B, 1997.
"Threshold Cointegration,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
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