Estimation of TAR Models
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) get 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 non-standard, but are available in closed form so critical values are readily available. To illustrate this theory, we report applications of these methods to TAR models fit to the U.S. unemployment rate and to the U.S. 3-month Treasury Bill rate. We find statistically significant threshold effects.
|Date of creation:||01 Jan 1996|
|Date of revision:|
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Boston College Working Papers in Economics
319., Boston College Department of Economics, revised 12 May 1998.
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Cowles Foundation Discussion Papers
1015, Cowles Foundation for Research in Economics, Yale University.
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RCER Working Papers
296, University of Rochester - Center for Economic Research (RCER).
- Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
- White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
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