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

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.

Bayesian Unit Root Test for AR(1) Model with Trend Approximated

“…[13] used the spline, Bayesian spline, and penalized spline regression methods to model the distribution graph of ratios of export to import for Turkey. [17] considered Buys-Ballot and classical methods of decomposing to estimate the cubic trend as well as other components of the times series and obtained the chain base and fixed base estimators with their statistical properties. [19] proposed a particle swarm optimization B-spline network to improve the prediction accuracy of non-linear time series.…”