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Robust Estimation and Inference for Threshold Models with Integrated Regressors

  • Haiqiang Chen
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    This paper studies the robust estimation and inference of threshold models with integrated regres- sors. We derive the asymptotic distribution of the profiled least squares (LS) estimator under the diminishing threshold effect assumption that the size of the threshold effect converges to zero. Depending on how rapidly this sequence converges, the model may be identified or only weakly identified and asymptotic theorems are developed for both cases. As the convergence rate is unknown in practice, a model-selection procedure is applied to determine the model identification strength and to construct robust confidence intervals, which have the correct asymptotic size irrespective of the magnitude of the threshold effect. The model is then generalized to incorporate endogeneity and serial correlation in error terms, under which, we design a Cochrane-Orcutt feasible generalized least squares (FGLS) estimator which enjoys efficiency gains and robustness against different error specifications, including both I(0) and I(1) errors. Based on this FGLS estimator, we further develop a sup-Wald statistic to test for the existence of the threshold effect. Monte Carlo simulations show that our estimators and test statistics perform well.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2013-034.pdf
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    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2013-034.

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    Length: 39 pages
    Date of creation: Jul 2013
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2013-034
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    Web page: http://sfb649.wiwi.hu-berlin.de
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    1. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
    2. Andrews, Donald W K & McDermott, C John, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," Review of Economic Studies, Wiley Blackwell, vol. 62(3), pages 343-60, July.
    3. repec:att:wimass:9419 is not listed on IDEAS
    4. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    5. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
    6. Jesus Gonzalo & Jean-Yves Pitarakis, 2006. "Threshold effects in cointegrating relationships," Economics Working Papers we20060621, Universidad Carlos III, Departamento de Economía.
    7. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    8. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
    9. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
    10. Jesús Gonzalo & Jean-Ives Pitarakis, 2010. "Regime specific predictability in predictive regressions," Economics Working Papers we097844, Universidad Carlos III, Departamento de Economía.
    11. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
    12. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    13. 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).
    14. Bruce E. Hansen & Mehmet Caner, 1997. "Threshold Autoregressions with a Unit Root," Boston College Working Papers in Economics 381, Boston College Department of Economics.
    15. Campbell, John & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Scholarly Articles 3122601, Harvard University Department of Economics.
    16. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    17. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    18. Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics 0503002, EconWPA, revised 15 Dec 2005.
    19. Park, Joon Y. & Hahn, Sang B., 1999. "Cointegrating Regressions With Time Varying Coefficients," Econometric Theory, Cambridge University Press, vol. 15(05), pages 664-703, October.
    20. Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1453-1490, October.
    21. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
    22. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
    23. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    24. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
    25. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-25, April-Jun.
    26. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    27. Choi, Chi-Young & Hu, Ling & Ogaki, Masao, 2008. "Robust estimation for structural spurious regressions and a Hausman-type cointegration test," Journal of Econometrics, Elsevier, vol. 142(1), pages 327-351, January.
    28. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 365-84, Oct.-Dec..
    29. Choi, In & Saikkonen, Pentti, 2010. "Tests For Nonlinear Cointegration," Econometric Theory, Cambridge University Press, vol. 26(03), pages 682-709, June.
    30. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
    31. Phillips, Peter C.B. & Hodgson, Douglas J., 1994. "Spurious Regression and Generalized Least Squares," Econometric Theory, Cambridge University Press, vol. 10(05), pages 967-968, December.
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