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A simple test for the equality of integration orders

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  • Hualde, Javier

Abstract

A necessary condition for two time series to be nontrivially cointegrated is the equality of their respective integration orders. Thus, it is standard practice to test for order homogeneity prior to testing for cointegration. Tests for the equality of integration orders are particular cases of more general tests of linear restrictions among memory parameters of different time series, for which asymptotic theory has been developed in parametric and semiparametric settings. However, most tests have been just developed in stationary and invertible settings, and, more importantly, many of them are invalid when the observables are cointegrated (because they involve inversion of an asymptotically singular matrix). We propose a general testing procedure which does not suffer from this serious drawback, and, in addition, it is very simple to compute, it covers the stationary/nonstationary and invertible/noninvertible ranges, and, as we show in a Monte Carlo experiment, it works well in finite samples.

Suggested Citation

  • Hualde, Javier, 2013. "A simple test for the equality of integration orders," Economics Letters, Elsevier, vol. 119(3), pages 233-237.
    • Handle: RePEc:eee:ecolet:v:119:y:2013:i:3:p:233-237
    DOI: 10.1016/j.econlet.2013.03.003
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    References listed on IDEAS

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    1. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series 449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    Cited by:

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    2. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," EconomiX Working Papers 2019-14, University of Paris Nanterre, EconomiX.
    3. Abakah, Emmanuel Joel Aikins & Caporale, Guglielmo Maria & Gil-Alana, Luis Alberiko, 2021. "Economic policy uncertainty: Persistence and cross-country linkages," Research in International Business and Finance, Elsevier, vol. 58(C).
    4. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
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    6. Adebola, Solarin Sakiru & Gil-Alana, Luis A. & Madigu, Godfrey, 2019. "Gold prices and the cryptocurrencies: Evidence of convergence and cointegration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1227-1236.
    7. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," Working Papers hal-04141871, HAL.
    8. Demetrescu, Matei & Kusin, Vladimir & Salish, Nazarii, 2022. "Testing for no cointegration in vector autoregressions with estimated degree of fractional integration," Economic Modelling, Elsevier, vol. 108(C).
    9. Yaya, OlaOluwa S & Gil-Alana, Luis A., 2018. "High and Low Intraday Commodity Prices: A Fractional Integration and Cointegration Approach," MPRA Paper 90518, University Library of Munich, Germany.
    10. Gilles de Truchis & Florent Dubois & Elena Ivona Dumitrescu, 2019. "Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems," Working Papers hal-04141882, HAL.
    11. Pierre Perron, 2017. "Unit Roots and Structural Breaks," Econometrics, MDPI, vol. 5(2), pages 1-3, May.
    12. Gilles de Truchis & Elena Ivona Dumitrescu & Florent Dubois, 2019. "Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems," EconomiX Working Papers 2019-15, University of Paris Nanterre, EconomiX.
    13. Dettoni, Robinson & Gil-Alana, Luis A. & Yaya, OlaOluwa S., 2024. "Stock market prices and Dividends in the US: Bubbles or Long-run equilibria relationships?," International Review of Financial Analysis, Elsevier, vol. 94(C).
    14. Wang, Bin & Wang, Man & Chan, Ngai Hang, 2015. "Residual-based test for fractional cointegration," Economics Letters, Elsevier, vol. 126(C), pages 43-46.
    15. Man Wang & Ngai Hang Chan, 2016. "Testing for the Equality of Integration Orders of Multiple Series," Econometrics, MDPI, vol. 4(4), pages 1-10, December.

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    More about this item

    Keywords

    Integration orders; Fractional differencing; Fractional cointegration;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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