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Narrow-Band Analysis of Nonstationary Processes

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Author Info
D Marinucci
Peter M Robinson

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Abstract

The behaviour of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or over one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic difference, and in particular we indicate how the behaviour of the mean and variance changes across the two-dimensional space of integration orders. The results employ only local-to-zero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be applied in fractional cointegration with unknown integration orders.

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File URL: http://sticerd.lse.ac.uk/dps/em/em421.pdf
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Publisher Info
Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2001/421.

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Date of creation: Jul 2001
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Handle: RePEc:cep:stiecm:/2001/421

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Related research
Keywords: Nonstationary processes; long-range dependence; least squares estimation; narrow-band estimation; cointegration analysis.;

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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.:
  1. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August. [Downloadable!]
  2. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September. [Downloadable!] (restricted)
  3. repec:cup:etheor:v:13:y:1997:i:5:p:692-745 is not listed on IDEAS
  4. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de España Working Papers 9617, Banco de España.
  5. 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)
  6. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March. [Downloadable!] (restricted)
  7. D Marinucci & Peter M Robinson, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," STICERD - Econometrics Paper Series /2000/408, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  8. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(05), pages 692-745, October. [Downloadable!]
Full references

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(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. Javier Hualde & Peter M. Robinson, 2002. "Root-n-Consistent Estimation of Weak Fractional Cointegration," Faculty Working Papers 08/02, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  2. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, EconWPA. [Downloadable!]
  3. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2005. "Fractional Cointegration And Aggregate Money Demand Functions," Economics and Finance Discussion Papers 05-01, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
    Other versions:
  4. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series /2001/420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  5. Hurvich, Cliiford & Wang, Yi, 2006. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 1413, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  6. Katsumi Shimotsu, 2003. "Exact Local Whittle Estimation of Fractionally Cointegrated Systems," Economics Discussion Papers 570, University of Essex, Department of Economics. [Downloadable!]
  7. M. Gerolimetto & Peter M Robinson, 2006. "Instrumental Variables Estimation of Stationaryand Nonstationary Cointegrating Regressions," STICERD - Econometrics Paper Series /2006/500, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  8. 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:
  9. Luis Gil-Alana, 2009. "Government Expenditures and Revenues: Evidence of Fractional Cointegration in an Asymmetric Modeling," International Advances in Economic Research, Springer, vol. 15(2), pages 143-155, May. [Downloadable!] (restricted)
  10. Uwe Hassler & Francesc Marmol & Carlos Velasco, 2002. "Residual Log-Periodogram Inference for Long-Run Relationships," Darmstadt Discussion Papers in Economics 115, Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology). [Downloadable!]
    Other versions:
  11. Javier Hualde & Peter M Robinson, 2006. "Root-N-Consistent Estimation Of Weakfractional Cointegration," STICERD - Econometrics Paper Series /2006/499, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  12. Carlos Pestana Barros & Luis Gil-Alana, 2006. "Eta: A Persistent Phenomenon," Defence and Peace Economics, Taylor and Francis Journals, vol. 17(2), pages 95-116, April. [Downloadable!] (restricted)
  13. Javier Hualde, 2005. "Unbalanced Cointegration," Faculty Working Papers 06/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  14. Javier Hualde & Peter M Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," STICERD - Econometrics Paper Series /2006/502, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  15. Peter M Robinson, 2007. "Multiple Local Whittle Estimation in StationarySystems," STICERD - Econometrics Paper Series /2007/525, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  16. Peter M Robinson, 2004. "The Distance between Rival Nonstationary Fractional Processes," STICERD - Econometrics Paper Series /2004/468, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  17. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation, Yale University, revised Sep 2003. [Downloadable!]
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