Algebraic Structures in the Decomposition of Mixed and Multiplicative Trend-Cycle Models

Abstract

In his study examines the algebraic foundations of mixed and multiplicative models in the decomposition of trend-cycle components within time series analysis. By leveraging algebraic structures, we explore how these models interact with seasonal patterns and variance distribution. The Buys-Ballot table is utilized to assess changes in row, column, and overall means and variances, particularly in cases where no trend is present. Our findings provide a theoretical framework for distinguishing the structural properties of mixed and multiplicative models, enhancing their application in time series modelling and forecasting