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Properties of the Buys-Ballot Estimates When Trend-Cycle Component of a Time Series Is Linear: Additive Case

Iheanyi S. Iwueze, Eleazar C. Nwogu, Jude C. Ajaraogu

Abstract


The Properties of the Buys-Ballot estimates of the linear trend-cycle component of a time series are discussed for the additive model in this study. The estimates are based on the marginal and overall averages of the Buys-Ballot Table (1847). Discussed are the Chain Based Estimation (CBE) method and the Fixed Based Estimation (FBE) method. Both methods were shown to be unbiased and consistent for the intercept and the slope. Added to the advantage of estimating the seasonal component without first isolating the trend, this study has also shown that the estimate of the error variance can be obtained without necessarily decomposing the series. A simulated numerical example was used to illustrate the methods.

Keywords


Trend-cycle component, seasonality, Buys-Ballot estimates, unbiasedness, consistency, efficiency.

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