Characteristics of Decomposition Model of Quadratic Trend Component: Multiplicative Case
Kelechukwu C. N. Dozie *
Department of Statistics, Imo State University, Owerri, Imo State, Nigeria.
Stephen O. Ihekuna
Department of Statistics, Imo State University, Owerri, Imo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents the characteristics of the decomposition model of quadratic trend component with emphasis on the multiplicative model. Therefore, the ultimate is to characterize the series that admit the multiplicative model while comparing them with those of the additive and mixed models. The method adopted in obtaining the estimators of the parameters are those proposed for the series that admits multiplicative model. The results indicate that Buys-Ballot estimates for both multiplicative and mixed models have characteristics different from that of the additive model. (1) The graphs of Figures show clearly that the pattern in the plots of the seasonal averages and standard deviations of both the multiplicative and mixed models depict the waves of a quadratic while that of additive model is linear. (2) The error variance of the multiplicative model is not known and needs to be estimated from data. While that of additive and mixed models, assumed equal to one.
Keywords: Decomposition model, quadratic curve, trend parameter, seasonal indices, Buys-Ballot table