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Journal of Time Series Econometrics

Editor-in-Chief: Hidalgo, Javier

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Mathematical Citation Quotient (MCQ) 2015: 0.04

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1941-1928
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Asymptotic Theory for Regressions with Smoothly Changing Parameters

Eric Hillebrand
  • Corresponding author
  • CREATES, Aarhus University, Aarhus, Denmark
  • Email:
/ Marcelo C. Medeiros
  • Department of Economics, Pontifical Catholic University of Rio De Janeiro, Rio de Janeiro, RJ, Brazil
  • Email:
/ Junyue Xu
  • MFE Program, Haas School of Business, University of California Berkeley, Berkeley, CA, USA
  • Email:
Published Online: 2013-04-30 | DOI: https://doi.org/10.1515/jtse-2012-0024

Abstract: We derive asymptotic properties of the quasi-maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual -rate and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data.

Keywords: regime switching; smooth transition regression; asymptotic theory

JEL Codes: C22

References

  • Amemiya, T. 1985. Advanced Econometrics. Cambridge: Harvard University Press.

  • Andrews, D. 1992. “Generic Uniform Convergence.” Econometric Theory 8: 241–57. [Crossref]

  • Andrews, D. W. K., and C. J. McDermott. 1995. “Nonlinear Econometric Models with Deterministically Trending Variables.” Review of Economic Studies 62: 343–60. [Crossref]

  • Areosa, W., M. McAleer, and M. Medeiros. 2011. “Moment-Based Estimation of Smooth Transition Regression Models with Endogenous Variables.” Journal of Econometrics 165: 100–11. [Web of Science] [Crossref]

  • Bai, J. 1997. “Estimating Multiple Breaks One at a Time.” Econometric Theory 13: 315–52. [Crossref]

  • Bai, J., and P. Perron. 1998. “Estimating and Testing Linear Models with Multiple Structural Changes.” Econometrica 66(1):47–78.

  • Billingsley, P. 1999. Convergence of Probability Measures, 2nd edn. New York: Wiley.

  • Chan, K. S., and H. Tong. 1986. “On Estimating Thresholds in Autoregressive Models.” Journal of Time Series Analysis 7: 179–90. [Crossref]

  • Davidson, J. 1994. Stochastic Limit Theory. Oxford: Oxford University Press.

  • Davies, R. B. 1977: “Hypothesis Testing When the Nuisance Parameter in Present Only Under the Alternative.” Biometrika 64: 247–54.

  • Davies, R. B. 1987. “Hypothesis Testing when the Nuisance Parameter in Present Only Under the Alternative.” Biometrika 74: 33–44.

  • Feder, P. 1975. “On Asymptotic Distribution Theory in Segmented Regression Problems—Identified Case.” Annals of Statistics 3: 49–83. [Crossref]

  • Hansen, B. E. 1996. “Inference when a Nuisance Parameter Is Not Identified Under the Null Hypothesis.” Econometrica 64: 413–30. [Crossref]

  • Li, W. K., S. Ling, and M. McAleer. 2002. “Recent Theoretical Results for Time Series Models with GARCH Errors.” Journal of Economic Surveys 16: 245–69. [Crossref]

  • Lin, C. F. J., and T. Teräsvirta. 1994. “Testing the Constancy of Regression Parameters Against Continuous Structural Change.” Journal of Econometrics 62: 211–28. [Crossref]

  • Ling, S., and M. McAleer. 2003. “Asymptotic Theory for a Vector ARMA-GARCH Model.” Econometric Theory 19: 280–310. [Web of Science]

  • Lundbergh, S., and T. Teräsvirta. 1998. “Modelling Economic High-Frequency Time Series with STAR-STGARCH Models.” Working Paper Series in Economics and Finance 291, Stockholm School of Economics.

  • Luukkonen, R., P. Saikkonen, and T. Teräsvirta. 1988. “Testing Linearity Against Smooth Transition Autoregressive Models.” Biometrika 75: 491–9. [Crossref]

  • McAleer, M., and M. Medeiros. 2008. “A Multiple Regime Smooth Transition Heterogenous Autoregressive Model for Long Memory and Asymmetries.” Journal of Econometrics 147: 104–19. [Crossref] [Web of Science]

  • Medeiros, M., E. Mendes, and L. Oxley. 2009. “Cointegrating Smooth Transition Regressions with a Stationary Transition Variable.” Discussion Paper, Department of Economics, Pontifical Catholic University of Rio de Janeiro.

  • Medeiros, M. C., and A. Veiga. 2003. “Diagnostic Checking in a Flexible Nonlinear Time Series Model.” Journal of Time Series Analysis 24: 461–82. [Crossref]

  • Medeiros, M. C., and A. Veiga. 2005. “A Flexible Coefficient Smooth Transition Time Series Model.” IEEE Transactions on Neural Networks 16: 97–113. [Crossref]

  • Mira, S., and A. Escribano. 2000. “Nonlinear Time Series Models: Consistency and Asymptotic Normality of NLS Under New Conditions.” In Nonlinear Econometric Modeling in Time Series Analysis, edited by W. A. Barnett, D. Hendry, S. Hylleberg, T. Teräsvirta, D. Tjøsthein, and A. Würtz, 119–64. Cambridge: Cambridge University Press.

  • Perron, P. 1989. “The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis.” Econometrica 57(6):1361–401.

  • Saikkonen, P., and I. Choi. 2004. “Cointegrating Smooth Transition Regressions.” Econometric Theory 20: 301–40.

  • Schwarz, G. 1978. “Estimating the Dimension of a Model.” Annals of Statistics 6: 461–4. [Crossref]

  • Shiryaev, A. 1996. Probability, 2nd edn. New York: Springer.

  • Strikholm, B. 2006. “Determining the Number of Breaks in a Piecewise Linear Regression Model.” Working Paper Series in Economics and Finance 648, Stockholm School of Economics.

  • Suarez-Fariñas, M., C. E. Pedreira, and M. C. Medeiros. 2004. “Local Global Neural Networks: A New Approach for Nonlinear Time Series Modeling.” Journal of the American Statistical Association 99: 1092–107.

  • Teräsvirta, T. 1994. “Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models.” Journal of the American Statistical Association 89: 208–18.

  • Teräsvirta, T. 1998. “Modelling Economic Relationships with Smooth Transition Regressions.” In Handbook of Applied Economic Statistics, edited by A. Ullah and D. E. A. Giles, 507–52. New York: Dekker.

  • Teräsvirta, T., D. Tjøstheim, and C. Granger. 2010. Modelling Nonlinear Economic Time Series. Oxford, UK: Oxford University Press.

  • van Dijk, D., T. Teräsvirta, and P. H. Franses. 2002. “Smooth Transition Autoregressive Models – A Survey of Recent Developments.” Econometric Reviews 21: 1–47.

About the article

Published Online: 2013-04-30


Note that, contrary to the work on multiple structural breaks, for each break there are two nuisance parameter ( and c) instead of one.


Citation Information: Journal of Time Series Econometrics, ISSN (Online) 1941-1928, ISSN (Print) 2194-6507, DOI: https://doi.org/10.1515/jtse-2012-0024. Export Citation

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