Basic Properties of Buys-ballot Seasonal Variances Estimates for Choice of Models in Time Series

Abstract

This article presents basic properties of Buys-Ballot estimates for seasonal variances for the mixed, multiplicative and additive models in time series. The emphasis is to characterize the basic properties of seasonal variances for purpose of choice of model. In this article, the method of seasonal variances with illustrative examples for choice of suitable models in time series decomposition is also considered. Results show that, seasonal variances of the Buys-Ballot estimates are for additive model 1) a product of trending parameter only 2) It is a product season j through the square of the seasonal indices  s2j and parameters through the square of the seasonal averages X-2.j  for multiplicative model 3) A constant multiple of the square of the seasonal indices  s2j for mixed model.