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Determining The Cointegrating Rank In Nonstationary Fractional Systems By The Exact Local Whittle Approach

Author

Listed:
  • Morten Ø. Nielsen

    (Queen's University and CREATES)

  • Katsumi Shimotsu

    (Department of Economics, Queen's University)

Abstract

We propose to extend the cointegration rank determination procedure of Robinson and Yajima (2002) to accommodate both (asymptotically) stationary and nonstationary fractionally integrated processes as the common stochastic trends and cointegrating errors by applying the exact local Whittle analysis of Shimotsu and Phillips (2005). The proposed method estimates the cointegrating rank by examining the rank of the spectral density matrix of the d-th differenced process around the origin, where the fractional integration order, d, is estimated by the exact local Whittle estimator. Similar to other semiparametric methods, the approach advocated here only requires information about the behavior of the spectral density matrix around the origin, but it relies on a choice of (multiple) bandwidth(s) and threshold parameters. It does not require estimating the cointegrating vector(s) and is easier to implement than regression-based approaches, but it only provides a consistent estimate of the cointegration rank, and formal tests of the cointegration rank or levels of confidence are not available except for the special case of no cointegration. We apply the proposed methodology to the analysis of exchange rate dynamics among a system of seven exchange rates. Contrary to both fractional and integer-based parametric approaches, which indicate at most one cointegrating relation, our results suggest three or possibly four cointegrating relations in the data.
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Suggested Citation

  • Morten Ø. Nielsen & Katsumi Shimotsu, 2006. "Determining The Cointegrating Rank In Nonstationary Fractional Systems By The Exact Local Whittle Approach," Working Paper 1029, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1029
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    References listed on IDEAS

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    More about this item

    Keywords

    Cointegration rank; fractional cointegration; fractional integration; long memory; nonstationarity; semiparametric estimation; exact local Whittle estimator;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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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