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Functional cointegration: definition and nonparametric estimation

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  • Pitarakis, Jean-Yves

Abstract

We formally define a concept of functional cointegration linking the dynamics of two time series via a functional coefficient. This is achieved through the use of a concept of summability as an alternative to I(1)'ness which is no longer suitable under nonlinear dynamics. We subsequently introduce a nonparametric approach for estimating the unknown functional coefficients. Our method is based on a piecewise local least squares principle and is computationally simple to implement. We establish its consistency properties and evaluate its performance in finite samples.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 38846.

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Date of creation: May 2012
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Handle: RePEc:pra:mprapa:38846

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Keywords: Functional Coefficients; Unit Roots; Cointegration; Piecewise Local Linear Estimation;

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  1. Ted Juhl, 2005. "Functional-coefficient models under unit root behaviour," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 197-213, 07.
  2. Ioannis Kasparis & Peter C. B. Phillips, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," University of Cyprus Working Papers in Economics 2-2009, University of Cyprus Department of Economics.
  3. Jesus Gonzalo & Jean-Yves Pitarakis, 2006. "Threshold effects in cointegrating relationships," Economics Working Papers we20060621, Universidad Carlos III, Departamento de Economía.
  4. Breitung, Jörg, 1998. "Rank tests for nonlinear cointegration," SFB 373 Discussion Papers 1998,65, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. In Choi & Pentti Saikkonen, 2004. "Testing linearity in cointegrating smooth transition regressions," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 341-365, December.
  6. Vanessa Berenguer Rico & Jesus Gonzalo, 2011. "Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes," Economics Working Papers we1115, Universidad Carlos III, Departamento de Economía.
  7. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
  8. Damla Şenturk & Hans-Georg Muller, 2005. "Covariate-adjusted regression," Biometrika, Biometrika Trust, vol. 92(1), pages 75-89, March.
  9. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
  10. Banerjee, Anurag, 2007. "A method of estimating the average derivative," Journal of Econometrics, Elsevier, vol. 136(1), pages 65-88, January.
  11. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June.
  12. Vanessa Berenguer Rico & Jesús Gonzalo, 2013. "Co-summability from linear to non-linear cointegration," Economics Working Papers we1312, Universidad Carlos III, Departamento de Economía.
  13. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
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