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ESTIMATION OF NONLINEAR ERROR CORRECTION MODELS

Published online by Cambridge University Press:  27 August 2010

Myung Hwan Seo
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Abstract

Asymptotic theory for the estimation of nonlinear vector error correction models that exhibit regime-specific short-run dynamics is developed. In particular, regimes are determined by the error correction term, and the transition between regimes is allowed to be discontinuous, as in, e.g., threshold cointegration. Several nonregular problems are resolved. First of all, consistency—square root n consistency for the cointegrating vector β—is established for the least squares estimation of this general class of models. Second, the convergence rates are obtained for the least squares of threshold cointegration, which are n3/2 and n for β and γ, respectively, where γ denotes the threshold parameter. This fast rate for β in itself is of practical relevance because, unlike in smooth transition models, the estimation error in β does not affect the estimation of short-run parameters. We also derive asymptotic distributions for the smoothed least squares estimation of threshold cointegration.

Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 2 , April 2011 , pp. 201 - 234
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

This research was supported through a grant from the Economic and Social Science Research Council. I thank the co-Editor and a referee, Anders Rahbek, and seminar participants in numerous places.

References

REFERENCES

Anderson, H.M. (1997) Transaction costs and non-linear adjustment towards equilibrium in the US treasury bill market. Oxford Bulletin of Economics and Statistics 59, 465–484.CrossRefGoogle Scholar
Andrews, D.W.K. (1987) Consistency in nonlinear econometric models: A generic uniform law of large numbers. Econometrica 55, 1465–1471.CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.CrossRefGoogle Scholar
Azuma, K. (1967) Weighted sums of certain dependent random variables. Tohoku Mathematical Journal, 2nd ser. 19, 357–367.CrossRefGoogle Scholar
Bai, J. & Perron, P. (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78.CrossRefGoogle Scholar
Balke, N. & Fomby, T. (1997) Threshold cointegration. International Economic Review 38, 627–645.CrossRefGoogle Scholar
Bec, F. & Rahbek, A. (2004) Vector equilibrium correction models with non-linear discontinuous adjustments. Econometrics Journal 7, 628–651.CrossRefGoogle Scholar
Chan, K.S. (1993) Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. Annals of Statistics 21, 520–533.CrossRefGoogle Scholar
Corradi, V.N., Swanson, R., & White, H. (2000) Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes. Journal of Econometrics 96, 39–73.CrossRefGoogle Scholar
de Jong, R.M. (2001) Nonlinear estimation using estimated cointegrating relations. Journal of Econometrics 101, 109–122.CrossRefGoogle Scholar
de Jong, R.M. (2002) Nonlinear minimization estimators in the presence of cointegrating relations. Journal of Econometrics 110, 241–259.CrossRefGoogle Scholar
Engle, R.F. & Granger, C.W.J. (1987) Co-integration and error correction: Representation, estimation, and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Escribano, A. (2004) Nonlinear error correction: The case of money demand in the United Kingdom (1878–2000). Macroeconomic Dynamics 8, 76–116.Google Scholar
Escribano, A. & Mira, S. (2002) Nonlinear error correction models. Journal of Time Series Analysis 23, 509–522.CrossRefGoogle Scholar
Gonzalo, J. & Pitarakis, J.-Y. (2006) Threshold effects in cointegrating relationships. Oxford Bulletin of Economics and Statistics 68, 813–833.CrossRefGoogle Scholar
Gonzalo, J. & Wolf, M. (2005) Subsampling inference in threshold autoregressive models. Journal of Econometrics 127, 209–233.CrossRefGoogle Scholar
Granger, C.W.J. (2001) Overview of nonlinear macroeconometric empirical models. Macroeconomic Dynamics 5, 466–481.CrossRefGoogle Scholar
Granger, C. & Terasvirta, T. (1993) Modelling Nonlinear Economic Relationships. Oxford University Press.CrossRefGoogle Scholar
Hansen, B. (1992) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–500.CrossRefGoogle Scholar
Hansen, B.E. (1999) Threshold effects in non-dynamic panels: Estimation, testing, and inference. Journal of Econometrics 93, 345–368.CrossRefGoogle Scholar
Hansen, B.E. (2000) Sample splitting and threshold estimation. Econometrica 68, 575–603.CrossRefGoogle Scholar
Hansen, B. & Seo, B. (2002) Testing for two-regime threshold cointegration in vector error correction models. Journal of Econometrics 110, 293–318.CrossRefGoogle Scholar
Horowitz, J.L. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60, 505–531.CrossRefGoogle Scholar
Kapetanios, G., Shin, Y. & Snell, A. (2006) Testing for cointegration in nonlinear smooth transition error correction models. Econometric Theory 22, 279–303.CrossRefGoogle Scholar
Kristensen, D. & Rahbek, A. (2010) Likelihood-based inference for cointegration with nonlinear error-correction. Journal of Econometrics 158, 78–94.CrossRefGoogle Scholar
Kurtz, T. & Protter, P. (1991) Weak limit theorems for stochastic integrals and stochastic differential equations. Annals of Probability 19, 1035–1070.CrossRefGoogle Scholar
Lo, M. & Zivot, E. (2001) Threshold cointegration and nonlinear adjustment to the law of one price. Macroeconomic Dynamics 5, 533–576.CrossRefGoogle Scholar
Michael, P., Nobay, A.R., & Peel, D.A. (1997) Transactions costs and nonlinear adjustment in real exchange rates: An empirical investigation. Journal of Political Economy 105, 862–879.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Handbook of Econometrics IV, pp. 2111–2245. North-Holland.CrossRefGoogle Scholar
Park, J. & Phillips, P. (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117–161.CrossRefGoogle Scholar
Pötscher, B.M. & Prucha, I.R. (1991) Basic structure of the asymptotic theory in dynamic nonlinear econometric models. I. Consistency and approximation concepts. Econometric Reviews 10, 125–216.Google Scholar
Psaradakis, Z., Sola, M., & Spagnolo, F. (2004) On Markov error-correction models, with an application to stock prices and dividends. Journal of Applied Econometrics 19, 69–88.CrossRefGoogle Scholar
Saikkonen, P. (1995) Problems with the asymptotic theory of maximum likelihood estimation in integrated and cointegrated systems. Econometric Theory 11, 888–911.CrossRefGoogle Scholar
Saikkonen, P. (2005) Stability results for nonlinear error correction models. Journal of Econometrics 127, 69–81.CrossRefGoogle Scholar
Saikkonen, P. (2008) Stability of regime switching error correction models under linear cointegration. Econometric Theory 24, 294–318.CrossRefGoogle Scholar
Seo, M. (2006) Bootstrap testing for the null of no cointegration in a threshold vector error correction model. Journal of Econometrics 134, 129–150.Google Scholar
Seo, M. & Linton, O. (2007) A smoothed least squares estimator for the threshold regression. Journal of Econometrics 141, 704–735.CrossRefGoogle Scholar
Sephton, P.S. (2003) Spatial market arbitrage and threshold cointegration. American Journal of Agricultural Economics 85, 1041–1046.Google Scholar
Taylor, A.M. (2001) Potential pitfalls for the purchasing power parity puzzle? Sampling and specification biases in mean-reversion tests of the law of one price. Econometrica 69, 473–498.CrossRefGoogle Scholar
Wooldridge, J.M. & White, H. (1988) Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometric Theory 4, 210–230.Google Scholar
Wu, C.-F. (1981) Asymptotic theory of nonlinear least squares estimation. Annals of Statistics 9, 501–513.CrossRefGoogle Scholar