English

AR and MA representation of partial autocorrelation functions, with applications

Spectral Theory 2007-05-23 v7 Probability

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.

Cite

@article{arxiv.math/0702648,
  title  = {AR and MA representation of partial autocorrelation functions, with applications},
  author = {Akihiko Inoue},
  journal= {arXiv preprint arXiv:math/0702648},
  year   = {2007}
}

Comments

Published in Probability Theory and Related Fields

R2 v1 2026-07-22T17:51:30.745Z