AR and MA representation of partial autocorrelation functions, with applications

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 th...

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Veröffentlicht in:	Probability theory and related fields 2008-03, Vol.140 (3-4), p.523-551
1. Verfasser:	Inoue, Akihiko
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic properties Autocorrelation functions Economics Exact sciences and technology Finance General topics Hilbert space Insurance Management Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Operations Research/Decision Theory Polynomials Probability Probability and statistics Probability Theory and Stochastic Processes Quantitative Finance Representations Sciences and techniques of general use Stationary processes Statistics for Business Stochastic processes Studies Theoretical
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Zusammenfassung:	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.
ISSN:	0178-8051 1432-2064
DOI:	10.1007/s00440-007-0074-1