The Annals of Statistics

Narrow-band analysis of nonstationary processes

D. Marinucci and P. M. Robinson

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 29, Number 4 (2001), 947-986.

Dates
First available in Project Euclid: 14 February 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1013699988

Digital Object Identifier
doi:10.1214/aos/1013699988

Mathematical Reviews number (MathSciNet)
MR1869235

Zentralblatt MATH identifier
1012.62100

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G18: Self-similar processes 62M15: Spectral analysis

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

Citation

Robinson, P. M.; Marinucci, D. Narrow-band analysis of nonstationary processes. Ann. Statist. 29 (2001), no. 4, 947--986. doi:10.1214/aos/1013699988. https://projecteuclid.org/euclid.aos/1013699988


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