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Testing for Linearity

  • Hansen, Bruce E

The problem of testing for linearity and the number of regimes in the context of self-exciting threshold autoregressive (SETAR) models is reviewed. We describe least-squares methods of estimation and inference. The primary complication is that the testing problem is non-standard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is non-standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications--annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes. Copyright 1999 by Blackwell Publishers Ltd

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Article provided by Wiley Blackwell in its journal Journal of Economic Surveys.

Volume (Year): 13 (1999)
Issue (Month): 5 (December)
Pages: 551-76

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Handle: RePEc:bla:jecsur:v:13:y:1999:i:5:p:551-76
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  1. Hansen, Bruce E., 1999. "Threshold effects in non-dynamic panels: Estimation, testing, and inference," Journal of Econometrics, Elsevier, vol. 93(2), pages 345-368, December.
  2. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(02), pages 222-259, April.
  3. 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.
  4. 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.
  5. Diebold, Francis X. & Chen, Celia, 1996. "Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures," Journal of Econometrics, Elsevier, vol. 70(1), pages 221-241, January.
  6. Jushan Bai, 1995. "Estimating Multiple Breaks One at a Time," Working papers 95-18, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
  8. Simon Burgess, 1991. "Nonlinear Dynamics in a Structural Model of Employment," CEP Discussion Papers dp0037, Centre for Economic Performance, LSE.
  9. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. 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.
  11. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S119-36, Suppl. De.
  12. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  13. repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
  14. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
  15. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Departmental Working Papers 9821, Bilkent University, Department of Economics.
  16. 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.
  17. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
  18. Rothman, Philip, 1988. "Further Evidence On The Asymmetric Behavior Of Unemployment Rates Over The Business Cycle," Working Papers 88-23, C.V. Starr Center for Applied Economics, New York University.
  19. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
  20. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
  21. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
  22. Galbraith, John W, 1996. "Credit Rationing and Threshold Effects in the Relation between Money and Output," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 419-29, July-Aug..
  23. Cao, C Q & Tsay, R S, 1992. "Nonlinear Time-Series Analysis of Stock Volatilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S165-85, Suppl. De.
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