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Fractional Cointegrating Regression In The Presence Of Linear Time Trends

Author

Listed:
  • Uwe Hassler

    (Free University of Berlin)

  • Francesc Marmol

    (University Carlos III of Madrid)

  • C. Velasco

    (University Carlos III of Madrid)

Abstract

We consider regressions of nonstationary fractionally integrated variables dominated by linear time trends. The regression errors can be short memory, long memory, or even nonstationary, and hence allow for a very flexible cointegration model. Our main contributions are two: First, we analyze the limiting behaviour of the regression estimators. We find in case of simple regressions that limiting normality arises at a rate of convergence that is independent of the order of integration of the regressor. This result does not carry over to the multivariate case, where the limiting distribution is more complicated. Second, we investigate a residual-based, log-periodogram regression. We state conditions that allow consistent estimation of the memory parameter of the error term. This estimator follows a limiting normal distribution and is therefore suitable for cointegration testing. The applicability of this asymptotic result to finite samples is established by means of Monte Carlo experiments.

Suggested Citation

  • Uwe Hassler & Francesc Marmol & C. Velasco, 2000. "Fractional Cointegrating Regression In The Presence Of Linear Time Trends," Computing in Economics and Finance 2000 138, Society for Computational Economics.
    • Handle: RePEc:sce:scecf0:138
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    References listed on IDEAS

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    1. Javier Hidalgo & Peter M Robinson, 1997. "Time Series Regression with Long Range Dependence - (Now published in 'Annals of Statistics', 25, (1997)pp.2054-2083.)," STICERD - Econometrics Paper Series 318, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Francesc Marmol & Juan J. Dolado, 1999. "Asymptotic Inference for Nonstationary Fractionally Integrated Processes," Computing in Economics and Finance 1999 513, Society for Computational Economics.
    3. Diebold, Francis X & Rudebusch, Glenn D, 1991. "Is Consumption Too Smooth? Long Memory and the Deaton Paradox," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 1-9, February.
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    11. Marmol, Francesc, 1997. "Fractional integration versus trend stationary in time series analysis," DES - Working Papers. Statistics and Econometrics. WS 10498, Universidad Carlos III de Madrid. Departamento de Estadística.
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    Cited by:

    1. Ingolf Dittmann, 2000. "Residual‐Based Tests For Fractional Cointegration: A Monte Carlo Study," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(6), pages 615-647, November.
    2. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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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