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.
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Length: 24 pages Date of creation: 01 Jan 1996 Date of revision: Handle: RePEc:boc:bocoec:325
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Find related papers by JEL classification: C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
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