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Estimation of TAR Models

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  • Bruce E. Hansen

    (Boston College)

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) 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.

Suggested Citation

  • Bruce E. Hansen, 1996. "Estimation of TAR Models," Boston College Working Papers in Economics 325., Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:325
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    References listed on IDEAS

    as
    1. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    3. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    4. 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.
    5. Tong, Howell, 2015. "Threshold models in time series analysis—Some reflections," Journal of Econometrics, Elsevier, vol. 189(2), pages 485-491.
    6. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    7. Terasvirta, Timo & Tjostheim, Dag & W.J. Granger, Clive, 1986. "Aspects of modelling nonlinear time series," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 48, pages 2917-2957, Elsevier.
    8. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
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    Citations

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    Cited by:

    1. González, M. & Gonzalo, Jesús, 1997. "Threshold unit root models," DES - Working Papers. Statistics and Econometrics. WS 6214, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Suman Gupta & Vinay Goyal & Vinay Kumar Kalakbandi & Sankarshan Basu, 2018. "Overconfidence, trading volume and liquidity effect in Asia’s Giants: evidence from pre-, during- and post-global recession," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 45(3), pages 235-257, September.
    3. Benbouziane, Mohamed & Benamar, Abdelhak, 2006. "The Purchasing Power Parity in The Maghreb Countries : A Nonlinear Perspective," MPRA Paper 13853, University Library of Munich, Germany, revised 2007.

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    More about this item

    Keywords

    TAR; threshold autoregression; Markov switching;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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