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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. Simon Burgess, 1991. "Nonlinear Dynamics in a Structural Model of Employment," CEP Discussion Papers dp0037, Centre for Economic Performance, LSE.
  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. Bruce E. Hansen, 1997. "Threshold effects in non-dynamic panels: Estimation, testing and inference," Boston College Working Papers in Economics 365, Boston College Department of Economics.
  4. 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.
  5. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(02), pages 222-259, April.
  6. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics 310., Boston College Department of Economics.
  7. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
  8. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9206, Tilburg - Center for Economic Research.
  9. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
  10. 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.
  11. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
  12. 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.
  13. 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.
  14. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June.
  15. 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.
  16. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  17. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  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. 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.
  24. repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
  25. 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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