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Estimation of long-run parameters in unbalanced cointegration

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  • Hualde, Javier
Abstract
This paper analyses the asymptotic properties of nonlinear least squares estimators of the long run parameters in a bivariate unbalanced cointegration framework. Unbalanced cointegration refers to the situation where the integration orders of the observables are different, but their corresponding balanced versions (with equal integration orders after filtering) are cointegrated in the usual sense. Within this setting, the long run linkage between the observables is driven by both the cointegrating parameter and the difference between the integration orders of the observables, which we consider to be unknown. Our results reveal three noticeable features. First, superconsistent (faster than n-consistent) estimators of the difference between memory parameters are achievable. Next, the joint limiting distribution of the estimators of both parameters is singular, and, finally, a modified version of the “Type II” fractional Brownian motion arises in the limiting theory. A Monte Carlo experiment and the discussion of an economic example are included.

Suggested Citation

  • Hualde, Javier, 2014. "Estimation of long-run parameters in unbalanced cointegration," Journal of Econometrics, Elsevier, vol. 178(2), pages 761-778.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:2:p:761-778
    DOI: 10.1016/j.jeconom.2013.10.014
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    Cited by:

    1. de Truchis, Gilles & Dell’Eva, Cyril & Keddad, Benjamin, 2017. "On exchange rate comovements: New evidence from a Taylor rule fundamentals model with adaptive learning," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 48(C), pages 82-98.
    2. S{o}ren Johansen & Morten {O}rregaard Nielsen, 2022. "Weak convergence to derivatives of fractional Brownian motion," Papers 2208.02516, arXiv.org, revised Oct 2022.
    3. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    4. 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.
    5. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," Working Papers hal-04141871, HAL.
    6. Gilles de Truchis & Florent Dubois & Elena Ivona Dumitrescu, 2019. "Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems," Working Papers hal-04141882, HAL.
    7. 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.

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    More about this item

    Keywords

    Unbalanced cointegration; Long run parameters; Nonlinear least squares; Type II fractional Brownian motion;
    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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