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.
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- 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.
- Balke, Nathan S. & Fomby, Thomas B., 1992.
9209, Federal Reserve Bank of Dallas.
- 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.
- Akram, Q. Farooq & Nymoen, Ragnar, 2006. "Econometric modelling of slack and tight labour markets," Economic Modelling, Elsevier, vol. 23(4), pages 579-596, July.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
- Campbell, John Y & Shiller, Robert J, 1987.
"Cointegration and Tests of Present Value Models,"
Journal of Political Economy,
University of Chicago Press, vol. 95(5), pages 1062-1088, October.
- John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
- 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.
- Campbell, John & Shiller, Robert, 1987. "Cointegration and Tests of Present Value Models," Scholarly Articles 3122490, Harvard University Department of Economics.
- 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.
- Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, December.
- Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1052-1090, December.
- 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.
- 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.
- 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.
- Catherine S. Forbes & Paul Kofman, 2000.
"Bayesian Target Zones,"
Research Paper Series
32, Quantitative Finance Research Centre, University of Technology, Sydney.
- Catherine S. Forbes & Paul Kofman, 2000. "Bayesian Target Zones," Econometric Society World Congress 2000 Contributed Papers 0575, Econometric Society.
- 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.
- 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 116-126, February.
- 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.
- 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.
- 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.
- Elias Tzavalis & Michael Wickens, "undated".
"The Rational Expectations Hypothesis of the Term Structure: reconciling the evidence,"
95/33, Department of Economics, University of York.
- Tzavalis, Elias & Wickens, Micheal, 1994. "The Rational Expectations Hypothesis of the Term Structure: Reconciling the Evidence," Discussion Papers 9402, Exeter University, Department of Economics.
- 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 465-484, November.
- Martin D. Evans & Karen K. Lewis, 1992.
"Do Stationary Risk Premia Explain It All? Evidence from the Term Structure,"
92-11, New York University, Leonard N. Stern School of Business, Department of Economics.
- 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.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, "undated".
"Multivariate GARCH models: a survey,"
CORE Discussion Papers RP
1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- 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.
- 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.
- repec:cup:etheor:v:23:y:2007:i:04:p:761-766 is not listed on IDEAS
- 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.
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