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Fractional cointegrating regressions in the presence of linear time trends

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  • Hassler, Uwe
  • Marmol, Francesc

Abstract

We consider regressions of nonstationary fractionally integrated variables dominated by linear time trends. The regression errors are short memory, long memory or even nonstationary, and hence allow for a very flexible cointegration model. In case of simple regressions, least squares estimation gives rise to limiting normal distribucions independently of the order of integration of the regressor, whereas the customary t-statistics diverge. We also investigate the possibility of testing for mean reverting equilibrium deviations by means of a residual-based log-periodogram regression. Asymptotic results become more complicated in the multivariate case.

Suggested Citation

  • Hassler, Uwe & Marmol, Francesc, 1998. "Fractional cointegrating regressions in the presence of linear time trends," DES - Working Papers. Statistics and Econometrics. WS 9794, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:9794
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    References listed on IDEAS

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    1. Francesc Marmol & Juan J. Dolado, 1999. "Asymptotic Inference for Nonstationary Fractionally Integrated Processes," Computing in Economics and Finance 1999 513, Society for Computational Economics.
    2. 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.
    3. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
    4. repec:bla:restud:v:57:y:1990:i:1:p:99-125 is not listed on IDEAS
    5. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Baillie, Richard T & Chung, Ching-Fan & Tieslau, Margie A, 1996. "Analysing Inflation by the Fractionally Integrated ARFIMA-GARCH Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 23-40, Jan.-Feb..
    8. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
    9. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
    10. Ooms, Marius & Hassler, Uwe, 1997. "On the effect of seasonal adjustment on the log-periodogram regression," Economics Letters, Elsevier, vol. 56(2), pages 135-141, October.
    11. Crato, Nuno & Rothman, Philip, 1994. "Fractional integration analysis of long-run behavior for US macroeconomic time series," Economics Letters, Elsevier, vol. 45(3), pages 287-291.
    12. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    13. 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.
    14. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    15. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
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    Cited by:

    1. Dittmann, Ingolf, 1998. "Residual-based tests for fractional cointegration: A Monte Carlo study," Technical Reports 1998,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Nonstationary regressors;

    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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