Best linear unbiased estimate using buys-ballot procedure when trend-cycle component is linear

The Best linear unbiased estimate (BLUE) of Buys-Ballot estimates when trend-cycle component is linear are discussed in this paper. The estimates are those proposed by Iwueze and Nwogu (2004). Discussed are the Chain Based Estimation (CBE) method and the Fixed Based Estimation (FBE) method. The variates for the CBE method were found to have constant mean and variance but are correlated with only one significant autocorrelation coefficient at lag one. The variates for the FBE method were found to have constant mean, non-constant variance but with constant autocorrelation coefficient at all lags. Because the CBE variates exhibit stationarity, Best Linear unbiased estimators of the slope and intercept were derived. Numerical examples were used to illustrate the methods.