An explicit representation of Verblunsky coefficients

Details An explicit representation of Verblunsky coefficients An explicit representation of Verblunsky coefficients

2011-09-21

arxiv.org/abs/1109.4513v1

Mathematics

Probability

8 pages

Scientific paper

10.1016/j.spl.2011.11.004

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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