An explicit representation of Verblunsky coefficients

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.

8 pages

References in corpus (2)

• AR and MA representation of partial autocorrelation functions, with applications
• Szegö's Theorem and its Probabilistic Descendants

Cited by in corpus (4)

• Multivariate prediction and matrix Szegö theory
• Baxter's inequality for finite predictor coefficients of multivariate long-memory stationary processes
• The intersection of past and future for multivariate stationary processes
• Exponential decay rate of partial autocorrelation coefficients of ARMA and short-memory processes