Characterisation of the Time Series Decomposition Models when the Trend-Cycle Component is Exponential
Eleazar C. Nwogu *
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
Iheanyi S. Iwueze
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
One of the greatest challenges in descriptive time series analysis is how to choose the appropriate model for any study data. This study aims to characterise the three decomposition models commonly used in descriptive time series analysis. The purpose is to provide basis for choosing the most appropriate model for any study data. The Buys-Ballot procedure, adopted for choosing the most appropriate model, is based on the row and column coefficients of variation of the study series presented in a Buys-Ballot table. When trend-cycle component is exponential, the study shows that (a) the row coefficient of variation follows the modified negative exponential for the Additive model, constant for the Mixed and cyclic for the Multiplicative models, (b) the column coefficient of variation follows the seasonal pattern for the additive model, constant for the mixed model and cyclic for the multiplicative models. It is therefore, recommended that the (a) Additive model be used whenever the row coefficients of variation is negative exponential and column coefficient of variation varies according to the seasonal pattern, (b) the mixed model be used whenever the row and column coefficients of variation are constant and (c) the multiplicative model be used when the row and column coefficients of variation are cyclic.
Keywords: Buys-ballot procedure, decomposition models, coefficient of variation, descriptive time series, study series