Buys-Ballot Technique for the Analysis of Time Series with a Cubic-Trend Component

Emmanuel Okereke

doi:10.19139/soic.v6i2.294

Emmanuel Okereke

DOI: https://doi.org/10.19139/soic.v6i2.294

Keywords: Buys-Ballot Methods, Cubic trend, auto correlation structure, pairwise-negatively correlated estimators, invertible third-order moving average model

Abstract

Time series, especially those with the cubic trend component, are encountered in many data analysis situations. The decomposition of such series into various components requires a method that can adequately estimate the cubic trend as well as other components of the series. In this study, the chain base, fixed base and classical methods of decomposition of time series with the cubic trend component are discussed with emphasis on the additive model. Chain base and fixed base estimators of the additive model parameters are derived. Basic properties of these two classes of estimators are equally determined. The derived chain base variables have the autocorrelation structure of an invertible third-order moving average model. The chain base estimators are found to be pairwise-negatively correlated estimators. Though the classical method and chain base method are both used for time series decomposition, the chain base method is recommended when a case of multicollinearity has been established.

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