A comparison of some of pattern identification methods for order determination of mixed ARMA models

Abstract

Model identification is a crucial step in time-series modelling. The orthodox Box–Jenkins (BJ) identification examines the patterns of the sample autocorrelation function (SACF) and the sample partial autocorrelation function (SPACF). However, for mixed ARMA processes, the SACF and SPACF often exhibit similar behaviour, which makes the identification much more difficult. Recently, identification methods using the patterns of some functions of the autocorrelations have been proposed to supplement the BJ methods. This paper studies some of these proposed procedures. Their performances for order selection of a mixed ARMA process are compared with an expert system in a simulation study. Comments on each individual identification method are also given.