Subsetting and Identification of Optimal Models in Generalized Bilinear Time Series Modelling

Abstract

Significant efforts have been made to study the theory of bilinear time series models, especially simple bilinear (BL) models. Much less efforts, however, have been made to identify optimal models in generalized bilinear models. Focus on optimal model identification; this study attempts to fill this gap. Full and subset generalized bilinear (SGBL) models are proposed and shown to be robust in achieving stationarity for all non-linear series. The parameters of the proposed 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 generalized bilinear models.

Keywords: Non-linear Least Square, Newton-Raphson, Algorithm, Parameters and Stationarity.

2000 Mathematics Subject Classification. Primary: 37M10, Secondary: 46N30