Narrow-band analysis of nonstationary processes
AbstractThe behavior 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 behavior 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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Bibliographic InfoPaper provided by London School of Economics and Political Science in its series Open Access publications from London School of Economics and Political Science with number http://eprints.lse.ac.uk/303/.
Date of creation: 2001
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Publication status: Published in Annals of statistics (2001) v.29, p.947-986
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- Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
- 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.
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