Inference in TAR Models

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Inference in TAR Models

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Bruce Hansen (Boston College)

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Bruce E. Hansen

Abstract

A distribution theory is developed for least-squares estimates of the threshold in Threshold Autoregressive (TAR) models. We find that if we let the threshold effect (the difference in slopes between the two regimes) become small as the sample size increases, then the asymptotic distribution of the threshold estimator is free of nuisance parameters (up to scale). Similarly, the likelihood ratio statistic for testing hypotheses concerning the unknown threshold is asymptotically free of nuisance parameters. These asymptotic distributions are nonstandard, but are available in closed form, so critical values are readily available. To illustrate this theory, we report an application to the U.S. unemployment rate. We find statistically significant threshold effects.

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Article provided by Berkeley Electronic Press in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 2 (1997)
Issue (Month): 1 ()
Pages: 1-14
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Handle: RePEc:bep:sndecm:2:1997:1:1-14

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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.:

Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
Other versions:
- Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation, Yale University. [Downloadable!]
Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July. [Downloadable!] (restricted)
Other versions:
- Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation, Yale University. [Downloadable!]

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