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.
Publié le : 2001-08-14
Classification:
Nonstationary processes,
long range dependence,
least squares estimation,
narrow-band estimation,
cointegration analysis,
62M10,
60G18,
62M15
@article{1013699988,
author = {Robinson, P. M. and Marinucci, D.},
title = {Narrow-band analysis of nonstationary processes},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 947-986},
language = {en},
url = {http://dml.mathdoc.fr/item/1013699988}
}
Robinson, P. M.; Marinucci, D. Narrow-band analysis of nonstationary processes. Ann. Statist., Tome 29 (2001) no. 2, pp. 947-986. http://gdmltest.u-ga.fr/item/1013699988/