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Article

ROBUST ESTIMATION AND INFERENCE FOR THRESHOLD MODELS WITH INTEGRATED REGRESSORS

  • Haiqiang Chen (a1)
Abstract

This paper studies the robust estimation and inference of threshold models with integrated regressors. 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.

Copyright
COPYRIGHT: © Cambridge University Press 2014 
Corresponding author
*Address correspondence to Haiqiang Chen, Xiamen University, Xiamen, Fujian 361005, China; e-mail: hc335@xmu.edu.cn.
References
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Andrews, D.W.K. & McDermott, C.J. (1995) Nonlinear econometric models with deterministically trending variables. Review of Economic Studies 62(3), 343–360.
Balke, N. & Fomby, T. (1997) Threshold cointegration. International Economics Review 8, 627–645.
Bierens, H. & Martins, L. (2010) Time-varying cointegration. Econometric Theory 26, 1453–1490.
Cai, Z., Li, Q., & Park, J.Y. (2009) Functional-coefficient models for nonstationary time series data. Journal of Econometrics 148, 101–113.
Campbell, J.Y. & Yogo, M. (2006) Efficient tests of stock return predictability. Journal of Financial Economics 81, 27–60.
Caner, M. & Hansen, B.E. (2001) Threshold autoregression with a unit root. Econometrica 69, 1555–1596.
Chan, K.S. (1993) Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. Annals of Statistics 21, 520–533.
Chen, H. (2013) Robust Estimation and Inference for Threshold Models with Integrated Regressors. Working papers, Xiamen University. Available at SSRN: http://ssrn.com/abstract=2287442.
Cheng, X. (2008) Robust Confidence Intervals in Nonlinear Regression under Weak Identification. Manuscript, Department of Economics, Yale University.
Choi, C.Y., Hu, L., & Ogaki, M. (2008) Robust estimation for structural spurious regressions and a Hausman-type cointegration test. Journal of Econometrics 142, 327–351.
Choi, I. & Saikkonen, P. (2010) Test of nonlinear cointegration. Econometric Theory 26, 682–709.
Durlauf, S.N. & Johnson, P.A. (1995) Multiple regimes and cross-country growth behavior. Journal of Applied Econometrics 10, 365–384.
Elliott, G. & Müller, U.K. (2007) Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141(2), 1196–1218.
Gao, J., King, M.L., Lu, Z., & Tjøstheim, D. (2009a) Specification testing in nonstationary time series autoregression. Annals of Statistics 37, 3893–3928.
Gao, J., King, M.L., Lu, Z., & Tjøstheim, D. (2009b) Nonparametric specification testing for nonlinear time series with nonstationarity. Econometric Theory 25, 1869–1892.
Gonzalo, J. & Pitarakis, J. (2002) Estimation and model selection based inference in single and multiple threshold models. Journal of Econometrics 110, 319–352.
Gonzalo, J. & Pitarakis, J.Y. (2006) Threshold effects in cointegrating regressions. Oxford Bulletin of Economics and Statistics 68, 813–833.
Gonzalo, J. & Pitarakis, J.Y. (2012) Regime specific predictability in predictive regressions. Journal of Business and Economic Statistics 30(2), 229–241.
Hansen, B.E. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64, 413–430.
Hansen, B.E. (1997) Inference in TAR models. Studies in Nonlinear Dynamics and Econometrics 2, 1–14.
Hansen, B.E. (2000) Sample splitting and threshold estimation. Econometrica 68, 575–603.
Li, D. & Ling, S.Q. (2012) On the least squares estimation of multiple-regime threshold autoregressive models. Journal of Econometrics 167, 240–253.
Marmer, V. (2008) Nonlinearity, nonstationarity, and spurious forecasts. Journal of Econometrics 142(1), 1–27.
Park, J.Y. (1992) Canonical cointegrating regressions. Econometrica 60, 119–143.
Park, J.Y. & Hahn, S. (1999) Cointegration regression with time varying coefficients. Econometric Theory 15, 664–703.
Park, J.Y. & Phillips, P.C.B. (2001) Nonlinear regressions with integrated time series. Econometrica 69(1), 117–161.
Perron, P. & Yabu, T. (2009) Testing for shifts in trend with an integrated or stationary noise component. Journal of Business and Economics Statistics 27(3), 369–396.
Phillips, P.C.B. & Durlauf, S.N. (1986) Multiple time series regression with integrated processes. Review of Economic Studies 53, 474–95.
Phillips, P.C.B. & Hansen, B.E. (1990) Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125.
Phillips, P.C.B. & Hodgson, D.J. (1994) Spurious regression and generalized least squares. Econometric Theory 10, 957–958.
Phillips, P.C.B. & Lee, J.H. (2013) Predictive regression under varying degrees of persistence and robust long-horizon regression. Journal of Econometrics 177(2), 250–264.
Phillips, P.C.B. & Park, J.Y. (1988) Asymptotic equivalence of ordinary least squares and generalized least squares in regressions with integrated regressors. Journal of the American Statistical Association 83, 111–115.
Potter, S.M. (1995) A nonlinear approach to US GNP. Journal of Applied Econometrics 10, 109–125.
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–20.
Seo, M. & Linton, O. (2007) A smoothed least squares estimator for threshold regression models. Journal of Econometrics 141, 704–735.
Shao, Q. & Lu, C. (1987) Strong approximation for partial sums of weakly dependent random variables. Scientia Sinica 15, 576–587.
Shi, X. & Phillips, P.C.B. (2012) Nonlinear cointegration regression under weak identification. Econometric Theory 28(1), 1–39.
Wang, Q. & Phillips, P.C.B. (2009) Structural nonparametric cointegrating regression. Econometrica 77(6), 1901–1948.
Yu, P. (2012) Likelihood estimation and inference in threshold regression. Journal of Econometrics 167, 274–294.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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