Comparison of Mixed and Multiplicative Models when Trend Cycle Component is Linear

The purpose of this study is to present the linear trend cycle component with the emphasis on the choice between mixed and multiplication models in time series analysis. Most of the existing studies have adequately dwelt more on choice of model between additive and multiplicative, with little or no regards to the mixed model. The main aim of this study is to compare the row, column and overall means and variances for mixed and multiplicative models using Buys-Ballot table for seasonal time series. Specific objectives are 1) to obtain and compare the expected values of means for mixed and multiplicative models 2) to estimate and compare trend parameters and seasonal indices (when there is no trend, that is (b = 0)). The study indicate that column variances ( ) of the Buys-Ballot table depends on the season j only through the square of the seasonal effect for mixed model and it is for multiplicative model, a quadratic function of the column j and square of the seasonal effect .