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Distribution-free Tests of Fractional Cointegration

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  • Javier Hualde

    () (Universidad de Navarra)

  • Carlos Velasco

    () (Universidad Carlos III)

Abstract

We propose tests of the null of spurious relationship against the alternative of fractional cointegration among the components of a vector of fractionally integrated time series. Our test statistics have an asymptotic chi-square distribution under the null and rely on GLS-type of corrections which control for the short run correlation of the weak dependent components of the fractionally integrated processes. We emphasize corrections based on nonparametric modelization of the innovations' autocorrelation, relaxing important conditions which are standard in the literature, and, in particular, being able to consider simultaneously (asymptotically) stationary or nonstationary processes. Relatively weak conditions on the corresponding short run and memory parameter estimates are assumed. The new tests are consistent with a divergence rate that, in most of the cases, as we show in a simple situation, depends on the cointegration degree. Finite-sample properties of the tests are analysed by means of a Monte Carlo experiment.

Suggested Citation

  • Javier Hualde & Carlos Velasco, 2006. "Distribution-free Tests of Fractional Cointegration," Faculty Working Papers 08/06, School of Economics and Business Administration, University of Navarra.
  • Handle: RePEc:una:unccee:wp0806
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    2. Javier Hualde, 2012. "Estimation of the cointegrating rank in fractional cointegration," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1205, Departamento de Economía - Universidad Pública de Navarra.
    3. Leschinski, Christian & Voges, Michelle & Sibbertsen, Philipp, 2018. "Integration and Disintegration of EMU Government Bond Markets," Hannover Economic Papers (HEP) dp-625, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    4. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    5. Avarucci, Marco & Velasco, Carlos, 2009. "A Wald test for the cointegration rank in nonstationary fractional systems," Journal of Econometrics, Elsevier, pages 178-189.
    6. Wang, Bin & Wang, Man & Chan, Ngai Hang, 2015. "Residual-based test for fractional cointegration," Economics Letters, Elsevier, vol. 126(C), pages 43-46.
    7. repec:eee:ecolet:v:156:y:2017:i:c:p:145-150 is not listed on IDEAS
    8. Paolo Santucci de Magistris & Federico Carlini, 2014. "On the identification of fractionally cointegrated VAR models with the F(d) condition," CREATES Research Papers 2014-43, Department of Economics and Business Economics, Aarhus University.
    9. Man Wang & Ngai Hang Chan, 2016. "Testing for the Equality of Integration Orders of Multiple Series," Econometrics, MDPI, Open Access Journal, vol. 4(4), pages 1-10, December.

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    Keywords

    35;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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