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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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  18. Baillie, R.T. & Bollerslev, T., 1993. "Cointegration, Fractional Cointegration, and Exchange RAte Dynamics," Papers 9103, Michigan State - Econometrics and Economic Theory.
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  22. Hassler, Uwe & Wolters, Jurgen, 1994. "On the power of unit root tests against fractional alternatives," Economics Letters, Elsevier, vol. 45(1), pages 1-5, May.
  23. 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.
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  25. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  26. Abdol Soofi, 1998. "A fractional cointegration test of purchasing power parity: the case of selected members of OPEC," Applied Financial Economics, Taylor & Francis Journals, vol. 8(6), pages 559-566.
  27. 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.
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  29. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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