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Residual Log-Periodogram Inference for Long-Run Relationships

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Author Info
Uwe Hassler () (Goethe-Universität Frankfurt am Main)
Francesc Marmol (Departamento de Estadistica y Econometria, Universidad Carlos III de Madrid)
Carlos Velasco (Departamento de Estadistica y Econometria, Universidad Carlos III de Madrid)

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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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Publisher Info
Paper provided by Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology) in its series Darmstadt Discussion Papers in Economics with number 115.

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Length: 44 pages
Date of creation: Nov 2002
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Handle: RePEc:tud:ddpiec:115

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Related research
Keywords: Fractional cointegration; semiparametric inference; limiting normality; long memory; non-stationarity; exchange rates;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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    Other versions:
  5. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series /2001/421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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    Other versions:
  9. Diebold, Francis X & Gardeazabal, Javier & Yilmaz, Kamil, 1994. " On Cointegration and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 727-35, June. [Downloadable!] (restricted)
    Other versions:
  10. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January. [Downloadable!] (restricted)
    Other versions:
  11. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May. [Downloadable!] (restricted)
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  15. P.M. Robinson & D. Marinucci, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 149-160, January. [Downloadable!] (restricted)
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  17. 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. [Downloadable!] (restricted)
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  20. 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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  22. Dolado, Juan J. & Marmol, Francesc, 1997. "On the properties of the Dickey-Pantula test against fractional alternatives," Economics Letters, Elsevier, vol. 57(1), pages 11-16, November. [Downloadable!] (restricted)
  23. Xiao, Zhijie, 1999. "A residual based test for the null hypothesis of cointegration," Economics Letters, Elsevier, vol. 64(2), pages 133-141, August. [Downloadable!] (restricted)
  24. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February. [Downloadable!]
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Nielsen, Morten Oe., . "Semiparametric Estimation in Time Series Regression with Long Range Dependence," Economics Working Papers 2002-17, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  2. Katsumi Shimotsu, 2003. "Exact Local Whittle Estimation of Fractionally Cointegrated Systems," Economics Discussion Papers 570, University of Essex, Department of Economics. [Downloadable!]
  3. Xu Cheng & Peter C. B. Phillips, 2009. "Cointegrating Rank Selection in Models with Time-Varying Variance," Cowles Foundation Discussion Papers 1688, Cowles Foundation, Yale University. [Downloadable!]
  4. 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. [Downloadable!]
    Other versions:
  5. Uwe Hassler & Jörg Breitung, 2002. "A Residual-Based LM Test for Fractional Cointegration," Darmstadt Discussion Papers in Economics 114, Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology). [Downloadable!]
  6. Morten Oerregaard Nielsen, . "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers 2002-8, School of Economics and Management, University of Aarhus. [Downloadable!]
  7. Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
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