Bruce E. Hansen
"Inference in TAR models", Studies in Nonlinear Dynamics and Econometrics,(1997), 2.
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 estimate 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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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111.
Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.