Statistical Properties of Buys-Ballot Estimates for Multiplicative Model with the Error Terms

Abstract

In this study, we discuss statistical properties of Buys-Ballot estimates for multiplicative model with their error terms. The aim of this study is to characterize the properties of the row, column and overall means and variances of the Buys-Ballot table for multiplicative model with the error terms. The properties of Buys-Ballot estimates in this study are used for (1) estimation of trend parameters (2) estimation of seasonal effect (3) choice of model for decomposition. The results indicate that (1) the column variance (\(\hat{\sigma}^2_j\)) of the Buys-Ballot depends on the seasonal indices (\(S^2_j\)) of the jth seasons. (2) the model that best describe the pattern in the transformed series is additive. This further confirms that the appropriate model of the original series is multiplicative.