Decomposition with the Additive Model Using Buys-Ballot Technique of Quadratic Trend-Cycle Component in Descriptive Time Series Analysis

Abstract

The study discusses decomposition with the additive model of quadratic trend-cycle in time series. Decomposition method is based on fitting a trend curve by some techniques and de-trending the series, using the de-trended series to adequately estimate and investigate the trend parameters, seasonal indices and residual component of the series. The method adopted in this study assumed that the series are arranged in a Buys-Ballot table with m rows and s columns. The study indicates that, the Buys-Ballot technique is computationally simple when compared with other descriptive techniques. The estimates of the quadratic trend-cycle component and seasonal effects are easily computed from periodic and seasonal averages. Hence, the computations are reduce to \(\hat{a}\) = 3.2051, \(\hat{b}\) = , 0.0218 and \(\hat{c}\) = -0.0001. Therefore, the fitted additive decomposition model is \(\hat{x}\)t = 3.2051+ 0.0218t - 0.0001t2 + \(\hat{s}\)t Under acceptable assumption, the article shows that additive model satisfies (\(\Sigma^s_{j=1}\) s\(_j\) = 0) as in equation (7). We also consider test for seasonality that admits additive model in this study.