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TESTING FOR COINTEGRATION IN NONLINEAR SMOOTH TRANSITION ERROR CORRECTION MODELS

Published online by Cambridge University Press:  09 February 2006

George Kapetanios ,
Yongcheol Shin  and
Andy Snell
George Kapetanios
Affiliation:
Queen Mary, University of London
Yongcheol Shin
Affiliation:
Leeds University Business School
Andy Snell
Affiliation:
Edinburgh School of Economics, University of Edinburgh
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Abstract

This paper proposes a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition process. In the context of nonlinear smooth transition error correction models (ECMs) we provide two simple operational versions of the tests. First, we obtain the associated nonlinear ECM-based tests. Second, we derive the nonlinear analogue of the residual-based test for cointegration in linear models. We derive the asymptotic distributions of the proposed tests. Monte Carlo simulation exercises confirm that our proposed tests have much better power than the linear counterparts against the alternative of a globally stationary nonlinear cointegrating process. In an application to the price-dividend relationship, our test is able to find cointegration, whereas the linear-based tests fail to do so.We are grateful to an associate editor, two anonymous referees, Richard Baillie, In Choi, Atanas Christev, Hira Koul, Richard Harris, Cheng Hsiao, Changjin Kim, Joon Park, Peter Schmidt, Yoonjae Whang, Jeff Wooldridge, and seminar participants at University of Edinburgh, Heriot-Watt University, Korea University, University of Leeds, Michigan State University, University of Newcastle, and Sungkunkwan University for their helpful comments. Partial financial support from the ESRC (grant R000223399) is gratefully acknowledged. The usual disclaimer applies.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 2 , April 2006 , pp. 279 - 303
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Arranz, M.A. & A. Escribano (2000) Cointegration testing in the presence of structural breaks. Oxford Bulletin of Economics and Statistics 62, 23–52.CrossRefGoogle Scholar
Balke, N.S. & T.B. Fomby (1997) Threshold cointegration. International Economic Review 38, 627–645.CrossRefGoogle Scholar
Banerjee, A., J.J. Dolado, & R. Mestre (1998) ECM tests for cointegration in a single equation framework. Journal of Time Series Analysis 19, 267–283.CrossRefGoogle Scholar
Bec, F., A. Guay, & E. Guerre (2004) Adaptive Consistent Unit Root Tests Based on Autoregressive Threshold Model. Manuscript, Crest-ENSAE.
Bec, F. & A. Rahbek (2004) Vector equilibrium correction models with nonlinear discontinuous adjustments. Econometrics 7, 628–651.CrossRefGoogle Scholar
Berk, K.N. (1974) Consistent autoregressive spectral estimates. Annals of Statistics 2, 489–502.CrossRefGoogle Scholar
Campbell, J.Y. & A. Kyle (1993) Smart money, noise trading and stock price behavior. Review of Economic Studies 60, 1–34.Google Scholar
Campbell, J.Y. & R.J. Shiller (1987) Cointegration and tests of present value models. Journal of Political Economy 95, 1062–1088.CrossRefGoogle Scholar
Campbell, J.Y. & R.J. Shiller (1988) Stock prices, earnings and expected dividends. Journal of Finance 43, 661–676.CrossRefGoogle Scholar
Caner, M. & B.E. Hansen (2001) Threshold autoregression with a unit root. Econometrica 69, 1555–1596.CrossRefGoogle Scholar
Choi, I. & P. Saikkonen (2004) Testing linearity in cointegrating smooth transition regressions. Econometrics Journal 7, 341–365.CrossRefGoogle Scholar
Corradi, V., N.R. Swanson, & H. White (2000) Testing for stationarity-ergodicity and for comovement between nonlinear discrete time Markov processes. Journal of Econometrics 96, 39–73.CrossRefGoogle Scholar
Cuthbertson, K., S. Hayes, & D. Nitzsche (1997) The behavior of the UK stock prices and returns: Is the market efficient? Economic Journal 107, 986–1008.Google Scholar
Davies, R.B. (1987) Hypothesis testing when a nuisance parameter is present under the alternative. Biometrika 74, 33–43.Google Scholar
Dickey, D.A. & W.A. Fuller (1979) Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431.Google Scholar
Enders, W. & C.W.J. Granger (1998) Unit root test and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16, 304–311.Google Scholar
Engle, R. & C.W.J. Granger (1987) Cointegration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Escribano, A. (1986) Identification and modelling of economic relationships in a growing economy. Ph.D Dissertation, University of California, San Diego.
Escribano, A. (2004) Nonlinear error correction: The case of money demand in the UK (1878–2000). Macroeconomic Dynamics 8, 76–116.CrossRefGoogle Scholar
Escribano, A. & S. Mira (2002) Nonlinear error correction models. Journal of Time Series Analysis 23, 509–522.CrossRefGoogle Scholar
Escribano, A. & G. Pfann (1998) Nonlinear error correction, asymmetric adjustment and cointegration. Economic Modelling 15, 197–216.CrossRefGoogle Scholar
Froot, K. & M. Obstfeld (1991) Intrinsic bubbles: The case of stock prices. American Economic Review 81, 1189–1214.Google Scholar
Gallagher, L.A. & M.P. Taylor (2001) Risky arbitrage, limits of arbitrage and nonlinear adjustment in the dividend-price ratio. Economic Inquiry 39, 524–536.CrossRefGoogle Scholar
Granger, C.W.J. & N.R. Swanson (1996) Further studies in the study of cointegrated variables. Oxford Bulletin of Economics and Statistics 58, 537–553.Google Scholar
Granger, C.W.J. & T. Teräsvirta (1993) Modelling Nonlinear Economic Relationships. Oxford University Press.
Hansen, B.E. (1995) Rethinking the univariate approach to unit root tests: How to use covariates to increase power. Econometric Theory 11, 1148–1171.CrossRefGoogle Scholar
Hansen, B.E. & B. Seo (2002) Testing for two-regime threshold cointegration in vector error correction models. Journal of Econometrics 110, 293–318.CrossRefGoogle Scholar
Johansen, S. (1995) Likelihood Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.
Kapetanios, G. & Y. Shin (2006) Unit root tests in three-regime SETAR models. Econometrics, in press.Google Scholar
Kapetanios, G., Y. Shin, & A. Snell (2003) Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359–379.CrossRefGoogle Scholar
Kiliç, R. (2003) A Testing Procedure for a Unit Root in the STAR Model. Manuscript, Georgia Institute of Technology.
Kremers, J.J.M., K.R. Ericsson, & J.J. Dolado (1992) The power of cointegration tests. Oxford Bulletin of Economics and Statistics 54, 325–348.CrossRefGoogle Scholar
Kyle, A.S. (1985) Continuous auctions and insider trading. Econometrica 53, 1315–1335.CrossRefGoogle Scholar
Luukkonen, R., P. Saikkonen, & T. Teräsvirta (1988) Testing linearity against smooth transition autoregressive models. Biometrika 75, 491–499.CrossRefGoogle Scholar
Michael, P., R.A. Nobay, & D.A. Peel (1997) Transactions costs and nonlinear adjustment in real exchange rates: An empirical investigation. Journal of Political Economy 105, 862–879.CrossRefGoogle Scholar
Ng, S. & P. Perron (1995) Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. Journal of the American Statistical Association 90, 268–281.CrossRefGoogle Scholar
Park, J.Y. & P.C.B. Phillips (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117–161.CrossRefGoogle Scholar
Pesaran, M.H., Y. Shin, & R.J. Smith (2001) Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics 16, 289–326.CrossRefGoogle Scholar
Phillips, P.C.B. & S. Ouliaris (1990) Asymptotic properties of residual based tests of cointegration. Econometrica 58, 165–193.CrossRefGoogle Scholar
Phillips, P.C.B. & V. Solo (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Psaradakis, Z., M. Sola, & F. Spagnolo (2004) On Markov error correction models with an application to stock prices and dividends. Journal of Applied Econometrics 19, 69–88.CrossRefGoogle Scholar
Said, S.E. & D.A. Dickey (1984) Testing for unit roots in ARMA models of unknown order. Biometrika 71, 599–607.CrossRefGoogle Scholar
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegrating regressions. Econometric Theory 7, 1–21.Google Scholar
Saikkonen, P. (2005) Stability results for nonlinear error correction models. Journal of Econometrics 127, 69–81.CrossRefGoogle Scholar
Saikkonen, P. & I. Choi (2004) Cointegrating smooth transition regressions. Econometric Theory 20, 301–340.CrossRefGoogle Scholar
Snell, A. & I. Tonks (1998) Testing for asymmetric information and inventory control effects in market maker behavior on the London Stock Exchange. Journal of Empirical Finance 5, 1–25.Google Scholar
Snell, A. & I. Tonks (2003) A theoretical analysis of institutional investors' trading costs in auction and dealer markets. Economic Journal 113, 576–598.Google Scholar
Taylor, M.P., D.A. Peel, & L. Sarno (2001) Nonlinearity in real exchange rates: Towards a solution of the purchasing power parity puzzles. International Economic Review 42, 1015–1042.CrossRefGoogle Scholar
van Dijk, D., T. Teräsvirta, & P.H. Franses (2002) Smooth transition autoregressive models—A survey of recent developments. Econometric Reviews 21, 1–47.Google Scholar