An explicit representation of Verblunsky coefficients
Probability
2011-11-10 v1 Classical Analysis and ODEs
Abstract
We prove a representation of the partial autocorrelation function (PACF) of a stationary process, or of the Verblunsky coefficients of its normalized spectral measure, in terms of the Fourier coefficients of the phase function. It is not of fractional form, whence simpler than the existing one obtained by the second author. We apply it to show a general estimate on the Verblunsky coefficients for short-memory processes as well as the precise asymptotic behaviour, with remainder term, of those for FARIMA processes.
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Cite
@article{arxiv.1109.4513,
title = {An explicit representation of Verblunsky coefficients},
author = {N. H. Bingham and Akihiko Inoue and Yukio Kasahara},
journal= {arXiv preprint arXiv:1109.4513},
year = {2011}
}
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8 pages