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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 cointegrated system is considered. We propose a two-step procedure that accommodates both (asymptotically) stationary (d =1/2) stochastic trend and/or equilibrium error. A tapered version of the local Whittle estimator of Robinson (2008) is used as the first-stage estimator, and the second-stage estimator employs the exact local Whittle approach of Shimotsu and Phillips (2005). The consistency and asymptotic distribution of the two-step estimator are derived. The estimator of the memory parameters has the same Gaussian asymptotic distribution in both the stationary and nonstationary case. The convergence rate and the asymptotic distribution of the estimator of the cointegrating vector are affected by the difference between the memory parameters. Further, the estimator has a Gaussian asymptotic distribution when the difference between the memory parameters is less than 1/2.

Suggested Citation

  • Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation of Fractionally Cointegrated Systems," Discussion Papers 2010-11, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2010-11
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    References listed on IDEAS

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    Cited by:

    1. Marcel Aloy & Gilles Truchis, 2016. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems and the Co-persistence Analysis of Stock Market Realized Volatilities," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 83-104, June.
    2. repec:eee:intfin:v:48:y:2017:i:c:p:82-98 is not listed on IDEAS
    3. de Truchis, Gilles & Dell’Eva, Cyril & Keddad, Benjamin, 2017. "On exchange rate comovements: New evidence from a Taylor rule fundamentals model with adaptive learning," Journal of International Financial Markets, Institutions and Money, Elsevier, pages 82-98.
    4. Stengos Thanasis & Yazgan M. Ege, 2014. "Persistence in real exchange rate convergence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 73-88, February.
    5. Charfeddine, Lanouar, 2016. "Breaks or long range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis," Economic Modelling, Elsevier, vol. 53(C), pages 354-374.
    6. de Truchis, Gilles & Keddad, Benjamin, 2013. "Southeast Asian monetary integration: New evidences from fractional cointegration of real exchange rates," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 26(C), pages 394-412.
    7. de Truchis, Gilles & Keddad, Benjamin, 2016. "On the risk comovements between the crude oil market and U.S. dollar exchange rates," Economic Modelling, Elsevier, pages 206-215.
    8. Christopoulos, Dimitris & McAdam, Peter, 2017. "Do financial reforms help stabilize inequality?," Journal of International Money and Finance, Elsevier, vol. 70(C), pages 45-61.
    9. Golinski, Adam & Madeira, Joao & Rambaccussing, Dooruj, 2014. "Fractional Integration of the Price-Dividend Ratio in a Present-Value Model of Stock Prices," SIRE Discussion Papers 2015-79, Scottish Institute for Research in Economics (SIRE).
    10. Thanasis Stengos & Ege Yazgan & Harun Ozkan, 2016. "Persistence in Convergence: Some further results," Working Papers 1605, University of Guelph, Department of Economics and Finance.
    11. Al-Shboul, Mohammad & Anwar, Sajid, 2016. "Fractional integration in daily stock market indices at Jordan's Amman stock exchange," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 16-37.
    12. Gilles Truchis & Benjamin Keddad, 2016. "Long-Run Comovements in East Asian Stock Market Volatility," Open Economies Review, Springer, vol. 27(5), pages 969-986, November.
    13. Clements, A.E. & Hurn, A.S. & Volkov, V.V., 2016. "Common trends in global volatility," Journal of International Money and Finance, Elsevier, vol. 67(C), pages 194-214.
    14. Dechert, Andreas, 2014. "Fraktionale Kointegrationsbeziehungen zwischen Euribor-Zinssätzen," W.E.P. - Würzburg Economic Papers 93, University of Würzburg, Chair for Monetary Policy and International Economics.
    15. Marcel Aloy & Gilles De Truchis, 2013. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems," Working Papers halshs-00879522, HAL.
    16. Stan Hurn & Peter C B Phillips & Shuping Shi, 2015. "Change Detection and the Casual Impact of the Yield Curve," NCER Working Paper Series 107, National Centre for Econometric Research.
    17. Gonçalves Mazzeu, Joao Henrique & González-Rivera, Gloria & Ruiz, Esther & Veiga, Helena, 2016. "A Bootstrap Approach for Generalized Autocontour Testing," DES - Working Papers. Statistics and Econometrics. WS 23457, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item

    Keywords

    discrete Fourier transform; fractional cointegration; long memory; nonstationarity; semiparametric estimation; Whittle likelihood;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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