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AR and MA representation of partial autocorrelation functions, with applications

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Title: AR and MA representation of partial autocorrelation functions, with applications
Authors: Inoue, Akihiko Browse this author
Keywords: partial autocorrelation functions
Verblunsky coefficients
orthogonal polynomials on the unit circle
Baxter's condition
fractional ARIMA processes
long memory
Issue Date: Mar-2008
Publisher: Springer
Journal Title: Probability Theory and Related Fields
Volume: 140
Issue: 3-4
Start Page: 523
End Page: 551
Publisher DOI: 10.1007/s00440-007-0074-1
Abstract: We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.
Rights: The original publication is available at
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 井上 昭彦

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