On the Relationship Between the S Array and the Box-Jenkins Method of ARMA Model Identification

Abstract

Abstract This paper investigates an extension of the partial autocorrelation function, which we call the generalized partial autocorrelation function. These generalized partial autocorrelations, which are not true correlations except when p = 0, are useful in examining the relationship between the S array method of Gray, Kelley, and McIntire (1978) and the Box-Jenkins approach to ARMA model identification. Also, the generalized partial autocorrelation is shown to be a useful model identification tool to be used along with the S array. Also discussed is a reformating of the S array into a shifted S array that the authors believe is easier to use in practice than the S array. The methods of this paper are illustrated by means of examples, including an analysis of the Makridakis (1978) metals series data.