Narrow-band analysis of nonstationary processes

D. Marinucci and Peter M. Robinson

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: The 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.

Keywords: Nonstationary processes; long range dependence; least squares estimation; narrow-band estimation; cointegration analysis. AMS 2000 subject classifications : Primary 62M10; secondary 60G18; 62M15. (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (67)

Published in Annals of Statistics, 2001, 29(4), pp. 947-986. ISSN: 0090-5364

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