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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.

Suggested Citation

  • Pitarakis, Jean-Yves, 2012. "Functional cointegration: definition and nonparametric estimation," MPRA Paper 38846, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:38846
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    References listed on IDEAS

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    1. repec:hrv:faseco:33077905 is not listed on IDEAS
    2. Jesús Gonzalo & Jean‐Yves Pitarakis, 2006. "Threshold Effects in Cointegrating Relationships," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 813-833, December.
    3. Damla Şenturk & Hans-Georg Muller, 2005. "Covariate-adjusted regression," Biometrika, Biometrika Trust, vol. 92(1), pages 75-89, March.
    4. 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.
    5. Ted Juhl, 2005. "Functional-coefficient models under unit root behaviour," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 197-213, July.
    6. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    7. In Choi & Pentti Saikkonen, 2004. "Testing linearity in cointegrating smooth transition regressions," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 341-365, December.
    8. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    9. Breitung, Jorg, 2001. "Rank Tests for Nonlinear Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 331-340, July.
    10. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(2), pages 213-221, June.
    11. Berenguer Rico, Vanessa & Gonzalo, Jesús, 2011. "Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes," UC3M Working papers. Economics we1115, Universidad Carlos III de Madrid. Departamento de Economía.
    12. Banerjee, Anurag, 2007. "A method of estimating the average derivative," Journal of Econometrics, Elsevier, vol. 136(1), pages 65-88, January.
    13. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    14. Berenguer Rico, Vanessa & Gonzalo, Jesús, 2013. "Co-summability from linear to non-linear cointegration," UC3M Working papers. Economics we1312, Universidad Carlos III de Madrid. Departamento de Economía.
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    Cited by:

    1. Guo-Liang Fan & Hong-Xia Xu & Zhen-Sheng Huang, 2016. "Empirical likelihood for semivarying coefficient model with measurement error in the nonparametric part," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(1), pages 21-41, January.

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    More about this item

    Keywords

    Functional Coefficients; Unit Roots; Cointegration; Piecewise Local Linear Estimation;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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