The Taylor property in non-negative bilinear models

TL;DR

This paper investigates the Taylor property in non-negative simple bilinear models, analyzing autocorrelations, error distributions, and leptokurtosis, with simulations to extend findings to real-valued models.

Contribution

It provides a detailed analysis of the Taylor property in non-negative bilinear models and explores its relation to leptokurtosis, including simulation studies for real-valued extensions.

Findings

Presence of the Taylor property depends on error distribution

Autocorrelation structures are characterized for stationary models

Simulation results support theoretical insights

Abstract

The aim of this paper is to discuss the presence of the Taylor property in the class of non-negative simple bilinear models. Considering strictly and weakly stationary models, we deduce autocorrelations of the process and of the square process and analyze the presence of the Taylor property considering several error process distributions. The relationship between the Taylor property and leptokurtosis of the corresponding bilinear process is discussed. 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.