Robinson, Peter M.: Narrow-Band Analysis of Nonstationary Processes
World Conference Econometric Society, 2000, Seattle

D. Marinucci, Universita la Sapienza
Peter M. Robinson, London School of Economics
Narrow-Band Analysis of Nonstationary Processes
Session: C-10-21  Tuesday 15 August 2000  by Robinson, Peter M.
The periodogram, and its average over a band of frequencies, was developed for the analysis of stationary time series, for example in spectrum estimation. However there is also interest in its performance in connection with nonstationary series, where it may not only be used inadvertantly, but also, as we show in the present paper, productively. We study the behaviour of averaged periodograms and cross-periodograms of a broad class of nonstationary processes. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones, and 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 on one that degenerates slowly to zero frequency as sample size increases, though some of our results also pertain to a nondegenerate subset of the Nyqvist band. In some cases it is found to make no asymptotic difference, and in particular we indicate how the behaviour 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 case of fractional cointegration with unknown integration orders.

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