Choice between Mixed and Multiplicative Models in Time Series Decomposition

This study discusses the condition(s) under which the mixed model best describes the pattern in an observed time series data, while comparing it with those of the additive and multiplicative models. Existing studies have focused on how to choose between additive and multiplicative models, with little or no emphasis on the mixed model. The ultimate objective of this study is therefore, to propose a statistical test for choosing between mixed and multiplicative models when the trending curve is linear. in descriptive time series analysis. The method adopted in this study is the Buys-Ballot procedure developed for choice of model by [1]. Results show that the column/seasonal variance of the Buys-Ballot table is, for the mixed model, a constant multiple of the square of seasonal effect and for the multiplicative model, a quadratic (in j) function of the square of the seasonal effects. Therefore, test for the choice between mixed and multiplicative models has been proposed based on the column/seasonal variances of the Buys-Ballot table. have been used to illustrate the applicability of the proposed test, Using empirical examples, the proposed test statistic identified the mixed model correctly in 98 out of the 100 simulations.