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Exact Local Whittle Estimation of Fractionally Cointegrated Systems

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  • Shimotsu, Katsumi

Abstract

Semiparametric estimation of a bivariate fractionally coitegrated system is considered. The new estimator employs the exact local Whittle approach developed by Shimotsu and Phillips (2003a) and estimates the two memory parameters jointly with the cointegrating vector. It permits both (asymptotically) stationary and nonstationary stochastic trends and/or equilibrium errors without relying on differencing or data tapering. Indeed, the asymptotic properties of the estimator depend only on the difference of the two memory parameters. The estimator of the memory parameters is shown to be consistent and asymptotically normally distributed in both stationary and nonstationary cases.

Suggested Citation

  • Shimotsu, Katsumi, 2003. "Exact Local Whittle Estimation of Fractionally Cointegrated Systems," Economics Discussion Papers 8869, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:8869
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    File URL: https://repository.essex.ac.uk/8869/
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    2. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    3. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    4. Morten Oerregaard Nielsen, "undated". "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers 2002-8, Department of Economics and Business Economics, Aarhus University.
    5. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    6. Carlos Velasco, 2003. "Gaussian Semi‐parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.
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    Cited by:

    1. Taro Takimoto & Yuzo Hosoya, 2004. "A Three‐Step Procedure For Estimating And Testing Cointegrated Armax Models," The Japanese Economic Review, Japanese Economic Association, vol. 55(4), pages 418-450, December.

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