AR and MA representation of partial autocorrelation functions, with applications

2007/02/28 by Akihiko Inoue · 18 citations
Economics, Econometrics and Finance · Mathematics · #Autocorrelation #Autocorrelation matrix #Autocorrelation technique #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Function (biology) #Partial autocorrelation function #Process (computing) #Representation (politics) #Spectral representation #Stochastic processes and financial applications #math.PR #math.SP #msc:42C05 #msc:60G10 #msc:62M10

paper · pdf · doi:10.1007/s00440-007-0074-1

published in Probability Theory and Related Fields 140(3-4), 523-551 (Springer Science+Business Media) · Published in Probability Theory and Related Fields

openalex publication_date 2007/04/26 · crossref created 2007/04/26 · crossref issued 2007/04/27 · crossref published 2007/04/27 · crossref published-online 2007/04/27 · arxiv created 2007/04/30 · crossref published-print 2008/03/01 · arxiv updated 2009/12/01 · crossref deposited 2024/02/13 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/05

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.

Citations

• The Asymptotic Behavior of the Prediction Error of a Stationary Sequence with a Spectral Density of Special Type
• AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING
• Long memory processes and fractional integration in econometrics
• Axioms for Euclidean Green's functions