Subsetting and identification of optimal models in one-dimensional bilinear time series modeling

Abstract

To date, significant efforts have been made to study the theory of bilinear time series models, especially simple bilinear models. Much less efforts, however, have been made to identify optimal models. Focused on optimal model identification, this study attempts to fill this gap. Full and subset one-dimensional bilinear models are proposed and shown to be robust in achieving stationarity for all non-linear series. The parameters of the models are estimated using robust nonlinear least-square method and Newton-Raphson iterative method, and statistical properties of the derived estimates are investigated. An algorithm is proposed to eliminate redundant parameters from full order bilinear models.