The Taylor Property in Bilinear Models

Abstract

The aim of this paper is to discuss the presence of the Taylor property in the class of simple bilinear models. Considering strictly and weakly stationary models, we deduce autocorrelations of the process and of its square and analyze the presence of the Taylor property in non-negative bilinear models considering several error process distributions, which are chosen according to the kurtosis value. For each one of these error process distributions, the class of parameterizations for the corresponding bilinear model satisfying Taylor property is obtained. The analysis of the relationship between the Taylor property and leptokurtosis in these bilinear processes allows to conclude that this property is a consequence of heavy tailed model distributions. With the goal of extending this research to real valued bilinear models, a simulation study is developed in a class of such models with symmetrical innovations.

Keywords

• bilinear models
• nonlinear time series
• stationarity
• Taylor property