Novel Insights into Estimation of Bilinear Time Series Models with Exponential and Symmetric Coefficients

Abstract

This paper focuses on the estimation and simulation of a specific subset of bilinear time series models characterized by dynamic exponential coefficients. Employing an exponential framework, we delve into the implications of the exponential function for our estimation process. Our primary aim is to estimate the coefficients of the proposed model using exponential coefficients derived from time-varying parameters. Through this investigation, our goal is to shed light on the asymptotic behaviors of the estimators and scrutinize their existence and probabilistic traits, drawing upon the foundational theorem established by Klimko and Nilsen. The least squares approach is pivotal in both estimating coefficients and analyzing estimator behavior. Moreover, we present a practical application to underscore the real-world implications of our research. By offering concrete examples of applications and simulations, we endeavor to provide readers with a comprehensive understanding of the implications of our work within the realm of time series analysis, specifically focusing on bilinear models and time-varying exponential coefficients. This multifaceted approach underscores the potential impact and practical relevance of our findings, contributing to the advancement of the field of time series analysis. To discern the symmetry characteristics of the model, we estimate it using coefficients that sum to zero and conduct a brief comparative analysis of two bilinear models.