AR and MA representation of partial autocorrelation functions, with applications

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128070We 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.Published in Probability Theory and Related FieldsSpectral TheoryProbability42C05; 62M10; 60G10AR and MA representation of partial autocorrelation functions, with applicationstext