An explicit representation of Verblunsky coefficients

N.H. Bingham, Akihiko Inoue and Yukio Kasahara

Statistics & Probability Letters, 2012, vol. 82, issue 2, 403-410

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 behavior, with remainder term, of those for FARIMA processes.

Keywords: Verblunsky coefficients; Partial autocorrelation functions; Phase functions; FARIMA processes; Long memory (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.11.004

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