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Inference on the Cointegration Rank in Fractionally Integrated Processes

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Author Info
Joerg Breitung and Uwe Hassler

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Abstract

For univariate time series we suggest a new variant of efficient score tests against fractional alternatives. This test has three important merits. First, by means of simulations we observe that it is superior in terms of size and power in some situations of practical interest. Second, it is easily understood and implemented as a slight modification of the Dickey-Fuller test, although our score test has a limiting normal distribution. Third and most important, our test generalizes to multivariate cointegration tests. Thus it allows to determine the cointegration rank of fractionally integrated time series. It does so by solving a generalized eigenvalue problem of the type proposed by Johansen (1988). However, the limiting distribution of the corresponding trace statistic is chi-squared, where the degrees of freedom depend only on the cointegration rank under the null hypothesis. The usefulness of the asymptotic theory for finite samples is established in a Monte Carlo experiment.

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Publisher Info
Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 233.

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Date of creation: 01 Apr 2001
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Handle: RePEc:sce:scecf1:233

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Related research
Keywords: Long memory; cointegration testing; trace statistic; limiting normality;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

References listed on IDEAS
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  1. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August. [Downloadable!]
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  4. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July. [Downloadable!] (restricted)
  7. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June. [Downloadable!] (restricted)
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  8. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January. [Downloadable!] (restricted)
  9. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October. [Downloadable!] (restricted)
  10. 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 103-12, January.
  11. Tsay, Wen-Jen, 2000. "Estimating Trending Variables In The Presence Of Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 16(03), pages 324-346, June. [Downloadable!]
  12. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August. [Downloadable!] (restricted)
  13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Laura Mayoral, 2005. "Further evidence on the statistical properties of Real GNP," Economics Working Papers 955, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2006. [Downloadable!]
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  2. Helmut LÜTKEPOHL, 2004. "Recent Advances in Cointegration Analysis," Economics Working Papers ECO2004/12, European University Institute. [Downloadable!]
  3. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus. [Downloadable!]
  4. Morten Ørregaard Nielsen, 2009. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," CREATES Research Papers 2009-02, School of Economics and Management, University of Aarhus. [Downloadable!]
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  5. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus. [Downloadable!]
  6. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2005. "Fractional Cointegration And Aggregate Money Demand Functions," Public Policy Discussion Papers 05-01, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
    Other versions:
  7. Juliane Scharff, 2007. "Inflation and the Divergence of Relative Prices: Evidence from a Cointegration Analysis," AStA Advances in Statistical Analysis, Springer, vol. 91(2), pages 141-158, August. [Downloadable!] (restricted)
  8. Ignacio N. Lobato & Carlos Velasco, 2005. "Efficient Wald Tests For Fractional Unit Roots," Economics Working Papers we056935, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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  9. Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  10. Morten Oerregaard Nielsen, . "Efficient Inference in Multivariate Fractionally Integrated Time Series Models," Economics Working Papers 2002-6, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  11. Avarucci, Marco & Velasco, Carlos, 2008. "A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems," Research Memoranda 049, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  12. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "Testing I(1) against I(d) alternatives in the presence of deteministic components," Economics Working Papers 957, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  13. Mauro Costantini & Roy Cerqueti, 2007. "Non parametric Fractional Cointegration Analysis," ISAE Working Papers 78, ISAE - Institute for Studies and Economic Analyses - (Rome, ITALY). [Downloadable!]
  14. Uwe Hassler & Francesc Marmol & Carlos Velasco, 2002. "Residual Log-Periodogram Inference for Long-Run Relationships," Darmstadt Discussion Papers in Economics 115, Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology). [Downloadable!]
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  15. Nielsen, Morten Oe., . "Multivariate Lagrange Multiplier Tests for Fractional Integration," Economics Working Papers 2002-18, School of Economics and Management, University of Aarhus. [Downloadable!]
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  16. Geetesh Bhardwaj & Norman Swanson, 2004. "An Empirical Investigation of the Usefulness of ARFIMA Models for Predicting Macroeconomic and Financial Time Series," Departmental Working Papers 200422, Rutgers University, Department of Economics. [Downloadable!]
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  17. Eduardo Rossi & Paolo Santucci de Magistris, 2009. "A No Arbitrage Fractional Cointegration Analysis Of The Range Based Volatility," CREATES Research Papers 2009-31, School of Economics and Management, University of Aarhus. [Downloadable!]
  18. Margherita Gerolimetto & Isabella Procidano, 2008. "A test for fractional cointegration using the sieve bootstrap," Statistical Methods and Applications, Springer, vol. 17(3), pages 373-391, July. [Downloadable!] (restricted)
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