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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.

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File URL: http://fmwww.bc.edu/EC-P/wp325.pdf
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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 325..

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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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Related research

Keywords: TAR; threshold autoregression; Markov switching;

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  1. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  2. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  3. 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.
  4. 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.
  5. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  6. 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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