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Narrow-Band Analysis of Nonstationary Processes

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  • D Marinucci
  • Peter M Robinson

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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Bibliographic 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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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

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

References

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  1. D Marinucci & Peter M. Robinson, 2000. "The averaged periodogram for nonstationary vector time series," LSE Research Online Documents on Economics 2294, London School of Economics and Political Science, LSE Library.
  2. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de Espa�a Working Papers 9617, Banco de Espa�a.
  3. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
  4. 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.
  5. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  6. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
  7. repec:cup:etheor:v:13:y:1997:i:5:p:692-745 is not listed on IDEAS
  8. 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.
  9. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(05), pages 692-745, October.
  10. 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.
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