First and second order non-linear cointegration models
This paper studies cointegration in non-linear error correction models characterized by discontinuous and regime-dependent error correction and variance specifications. In addition the models allow for autoregressive conditional heteroscedasticity (ARCH) type specifications of the variance. The regime process is assumed to depend on the lagged disequilibrium, as measured by the norm of linear stable or cointegrating relations. The main contributions of the paper are: i) conditions ensuring geometric ergodicity and nite second order moment of linear long run equilibrium relations and differenced observations, ii) a representation theorem similar to Granger's representations theorem and a functional central limit theorem for the common trends, iii) to establish that the usual reduced rank regression estimator of the cointegrating vector is consistent even in this highly extended model, and iv) asymptotic normality of the parameters for xed cointegration vector and regime parameters. Finally, an application of the model to US term structure data illustrates the empirical relevance of the model.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Frédérique Bec & Alain Guay & Emmanuel Guerre, 2002.
"Adaptive Consistent Unit Root Tests Based on Autoregressive Threshold Model,"
2002-46, Centre de Recherche en Economie et Statistique.
- Bec, Frederique & Guay, Alain & Guerre, Emmanuel, 2008. "Adaptive consistent unit-root tests based on autoregressive threshold model," Journal of Econometrics, Elsevier, vol. 142(1), pages 94-133, January.
- Corradi, V. & Swanson, N. & White, H., 1996.
"Testing for Stationarity-Ergodicity and for Comovements Between Nonlinear Discrete Time Markov Processes,"
4-96-6, Pennsylvania State - Department of Economics.
- Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
- Balke, Nathan S & Fomby, Thomas B, 1997.
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
- Nathan S. Balke & Thomas B. Fomby, 1992. "Threshold cointegration," Research Paper 9209, Federal Reserve Bank of Dallas.
- Tom Doan, . "RATS programs to replicate Balke-Fomby threshold cointegration," Statistical Software Components RTZ00010, Boston College Department of Economics.
- Krolzig, Hans-Martin & Marcellino, Massimiliano & Mizon, Grayham E., 2000.
"A Markov-switching vector equilibrium correction model of the UK labour market,"
Discussion Paper Series In Economics And Econometrics
0105, Economics Division, School of Social Sciences, University of Southampton.
- Massimiliano Marcellino & Grayham E. Mizon & Hans-Martin Krolzig, 2002. "A Markov-switching vector equilibrium correction model of the UK labour market," Empirical Economics, Springer, vol. 27(2), pages 233-254.
- Hans-Martin Krolzig & Massimiliano Marcellino & Grayham E. Mizon, . "A Markov-Switching Vector Equilibrium Correction Model of the UK Labour Market," Working Papers 185, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- Lu, Zudi, 1996. "A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 305-311, November.
- Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006.
"Multivariate GARCH models: a survey,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Catherine S. Forbes & Paul Kofman, 2000.
"Bayesian Target Zones,"
Econometric Society World Congress 2000 Contributed Papers
0575, Econometric Society.
- Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1052-1090, December.
- Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
- Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
- Anderson, Heather M, 1997. "Transaction Costs and Non-linear Adjustment towards Equilibrium in the US Treasury Bill Market," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(4), pages 465-84, November.
- John Y. Campbell & Robert J. Shiller, 1986.
"Cointegration and Tests of Present Value Models,"
Cowles Foundation Discussion Papers
785, Cowles Foundation for Research in Economics, Yale University.
- John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
- Campbell, John & Shiller, Robert, 1987. "Cointegration and Tests of Present Value Models," Scholarly Articles 3122490, Harvard University Department of Economics.
- Akram, Q. Farooq & Nymoen, Ragnar, 2006. "Econometric modelling of slack and tight labour markets," Economic Modelling, Elsevier, vol. 23(4), pages 579-596, July.
- Tzavalis, Elias & Wickens, Micheal, 1994.
"The Rational Expectations Hypothesis of the Term Structure: Reconciling the Evidence,"
9402, Exeter University, Department of Economics.
- Elias Tzavalis & Michael Wickens, . "The Rational Expectations Hypothesis of the Term Structure: reconciling the evidence," Discussion Papers 95/33, Department of Economics, University of York.
- Escribano, Alvaro, 2004. "Nonlinear Error Correction: The Case Of Money Demand In The United Kingdom (1878 2000)," Macroeconomic Dynamics, Cambridge University Press, vol. 8(01), pages 76-116, February.
- Saikkonen, Pentti, 2008. "Stability Of Regime Switching Error Correction Models Under Linear Cointegration," Econometric Theory, Cambridge University Press, vol. 24(01), pages 294-318, February.
- Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February.
- Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
- repec:cup:etheor:v:23:y:2007:i:04:p:761-766 is not listed on IDEAS
- Yacine Ait-Sahalia, 1995.
"Testing Continuous-Time Models of the Spot Interest Rate,"
NBER Working Papers
5346, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
- Forbes, C.S. & Kofman, P., 2000. "Bayesian Soft Target Zones," Monash Econometrics and Business Statistics Working Papers 4/00, Monash University, Department of Econometrics and Business Statistics.
- Evans, Martin D. D. & Lewis, Karen K., 1994.
"Do stationary risk premia explain it all?: Evidence from the term structure,"
Journal of Monetary Economics,
Elsevier, vol. 33(2), pages 285-318, April.
- Martin D. Evans & Karen K. Lewis, 1992. "Do Stationary Risk Premia Explain It All? Evidence from the Term Structure," Working Papers 92-11, New York University, Leonard N. Stern School of Business, Department of Economics.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Jensen, S ren Tolver & Rahbek, Anders, 2007. "On The Law Of Large Numbers For (Geometrically) Ergodic Markov Chains," Econometric Theory, Cambridge University Press, vol. 23(04), pages 761-766, August.
- Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2006. "Testing For Cointegration In Nonlinear Smooth Transition Error Correction Models," Econometric Theory, Cambridge University Press, vol. 22(02), pages 279-303, April.
When requesting a correction, please mention this item's handle: RePEc:aah:create:2009-04. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.