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Residual Log-Periodogram Inference for Long-Run-Relationships

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  • Hassler, Uwe
  • Marmol, Francesc
  • Velasco, Carlos

Abstract

We assume that some consistent estimator of an equilibrium relation between non-stationary fractionally integrated series is used in a first step to compute residuals (or differences thereof). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate and test the degree of persistence of the equilibrium deviation. Provided the first step estimator converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of persistence from residuals. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on the persistence. Our assumptions allow for stationary deviations with long memory as well as for non-stationary but transitory equilibrium errors. In particular, in case of several regressors we consider the joint estimation of the memory parameters of the observed series and of the equilibrium deviation. Wald statistics to test for parameter restrictions of the system have a limiting chi-squared distribution. We also analyze the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics.

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Bibliographic Info

Paper provided by Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL) in its series Darmstadt Discussion Papers in Economics with number 37317.

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Date of creation: Jun 2002
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Publication status: Published in Darmstadt Discussion Papers in Economics . 115 (2002-06)
Handle: RePEc:dar:ddpeco:37317

Note: for complete metadata visit http://tubiblio.ulb.tu-darmstadt.de/37317/
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Keywords: Fractional cointegration; semiparametric inference; limiting normality; long memory; non-stationarity; exchange rates.;

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References

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  24. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-27, October.
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Citations

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Cited by:
  1. Marcel Aloy & Gilles De Truchis, 2013. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems," Working Papers halshs-00879522, HAL.
  2. Kellard, Neil & Sarantis, Nicholas, 2008. "Can exchange rate volatility explain persistence in the forward premium?," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 714-728, September.
  3. Marcel Aloy & Mohamed Boutahar & Karine Gente & Anne Peguin-Feissolle, 2010. "Fractional integration and cointegration in stock prices and exchange rates," Working Papers halshs-00536140, HAL.
  4. Shimotsu, Katsumi, 2012. "Exact local Whittle estimation of fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 169(2), pages 266-278.
  5. Fabrizio Iacone & Peter M Robinson, 2004. "Cointegration in Fractional Systems with Deterministic Trends," STICERD - Econometrics Paper Series /2004/476, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. Davidson, James & Sibbertsen, Philipp, 2005. "Tests of Bias in Log-Periodogram Regression," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-317, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  7. Xu Cheng & Peter C. B. Phillips, 2009. "Cointegrating Rank Selection in Models with Time-Varying Variance," Cowles Foundation Discussion Papers 1688, Cowles Foundation for Research in Economics, Yale University.
  8. Morten Orregaard Nielsen, 2005. "Semiparametric Estimation in Time-Series Regression with Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 279-304, 03.
  9. Kellard, Neil & Dunis, Christian & Sarantis, Nicholas, 2010. "Foreign exchange, fractional cointegration and the implied-realized volatility relation," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 882-891, April.
  10. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
  11. repec:ebl:ecbull:v:30:y:2010:i:1:p:115-129 is not listed on IDEAS
  12. Fabrizio Iacone & Peter M. Robinson, 2004. "Cointegration in fractional systems with deterministic trends," LSE Research Online Documents on Economics 2232, London School of Economics and Political Science, LSE Library.
  13. Morten Oerregaard Nielsen, . "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers 2002-8, School of Economics and Management, University of Aarhus.
  14. Hassler, Uwe & Breitung, Jörg, 2002. "A Residual-Based LM Test for Fractional Cointegration," Darmstadt Discussion Papers in Economics 37318, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
  15. Coakley, Jerry & Dollery, Jian & Kellard, Neil, 2008. "The role of long memory in hedging effectiveness," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3075-3082, February.

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