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August 2001 Narrow-band analysis of nonstationary processes
D. Marinucci, P. M. Robinson
Ann. Statist. 29(4): 947-986 (August 2001). DOI: 10.1214/aos/1013699988


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.


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D. Marinucci. P. M. Robinson. "Narrow-band analysis of nonstationary processes." Ann. Statist. 29 (4) 947 - 986, August 2001.


Published: August 2001
First available in Project Euclid: 14 February 2002

zbMATH: 1012.62100
MathSciNet: MR1869235
Digital Object Identifier: 10.1214/aos/1013699988

Primary: 62M10
Secondary: 60G18 , 62M15

Keywords: cointegration analysis , Least squares estimation , Long range dependence , narrow-band estimation , nonstationary processes

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 4 • August 2001
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