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Estimation Of Nonlinear Error Correction Models

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  • Hwan Seo, Myung

Abstract

Asymptotic inference in nonlinear vector error correction models (VECM) thatexhibit regime-specific short-run dynamics is nonstandard and complicated. Thispaper contributes the literature in several important ways. First, we establish theconsistency of the least squares estimator of the cointegrating vector allowing forboth smooth and discontinuous transition between regimes. This is a nonregularproblem due to the presence of cointegration and nonlinearity. Second, we obtainthe convergence rates of the cointegrating vector estimates. They differ dependingon whether the transition is smooth or discontinuous. In particular, we find that therate in the discontinuous threshold VECM is extremely fast, which is n^{3/2},compared to the standard rate of n: This finding is very useful for inference onshort-run parameters. Third, we provide an alternative inference method for thethreshold VECM based on the smoothed least squares (SLS). The SLS estimatorof the cointegrating vector and threshold parameter converges to a functional of avector Brownian motion and it is asymptotically independent of that of the slopeparameters, which is asymptotically normal.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 02 (April)
Pages: 201-234

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Handle: RePEc:cup:etheor:v:27:y:2011:i:02:p:201-234_00

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  1. Oliver Linton & Myunghwan Seo, 2005. "A smoothed least squares estimator for threshold regression models," LSE Research Online Documents on Economics 4434, London School of Economics and Political Science, LSE Library.
  2. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
  3. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
  4. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
  5. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
  6. Myung Hwan Seo, 2005. "Unit root test in a threshold autoregression: asymptotic theory and residual-based block bootstrap," LSE Research Online Documents on Economics 6836, London School of Economics and Political Science, LSE Library.
  7. repec:rus:hseeco:2156 is not listed on IDEAS
  8. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  9. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  10. Corradi, V. & Swanson, N. & White, H., 1996. "Testing for Stationarity-Ergodicity and for Comovements Between Nonlinear Discrete Time Markov Processes," Papers 4-96-6, Pennsylvania State - Department of Economics.
  11. de Jong, Robert M., 2001. "Nonlinear estimation using estimated cointegrating relations," Journal of Econometrics, Elsevier, vol. 101(1), pages 109-122, March.
  12. Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2004. "On Markov error-correction models, with an application to stock prices and dividends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(1), pages 69-88.
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Cited by:
  1. Marçal, Emerson Fernandes & Valls Pereira, Pedro L., 2012. "Evaluating the existence of structural change in the brazilian term structure of interest : evidence based on cointegration models with structural break," Textos para discussão 314, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  2. Boonsoo Koo & Myung Hwan Seo, 2013. "Structural-break models under mis-specification: implications for forecasting," Monash Econometrics and Business Statistics Working Papers 11/13, Monash University, Department of Econometrics and Business Statistics.
  3. Woo, Kai-Yin & Lee, Shu-Kam & Chan, Alan, 2014. "Non-linear adjustments to intranational PPP," Journal of Macroeconomics, Elsevier, vol. 40(C), pages 360-371.
  4. Dennis Kristensen & Anders Rahbek, 2007. "Likelihood-Based Inference in Nonlinear Error-Correction Models," CREATES Research Papers 2007-38, School of Economics and Management, University of Aarhus.

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