The Expected Values of Buys-Ballot Estimates for Multiplicative Model with the Error Terms

The expected values of Buys-Ballot estimates with the error terms for multiplicative model in time series decomposition when trend-cycle component is linear is discussed. The expected values of Buys-Ballot estimates of row, column and overall means with the error terms are derived. A real example for the linear case is applied to determine the estimation of trend parameters, seasonal indices, choice of appropriate transformation and choice of model of the Buys-Ballot table. Results show that, the expected values of periodic and seasonal means of the Buys-Ballot table are; (1) periodic mean mimic the shape of the trending curves of the original series and contains seasonal indices (2) seasonal mean is a function of the trending parameters of the original series and contain seasonal indices.