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.
Highlights
One of the tasks frequently performed by time series analysts is the decomposition of a given time series into its various components
We compare the method with the classical decomposition method (CDM) through the decomposition of a real time series data set
The prediction accuracy measures employed in this work are the mean squared error (MSE), mean absolute error(MAE) and mean absolute percentage error (MAPE)
Summary
One of the tasks frequently performed by time series analysts is the decomposition of a given time series into its various components. The classical decomposition method is the first known method of decomposing time series. Its application is often predicated on the additive and multiplicative models. The objectives of the classical decomposition method have been mentioned in numerous studies. It helps us to investigate the presence of trend, seasonal and cyclical effects in a time series. Estimates of the four components of time series which include trend, seasonal, cyclical and irregular components are found with the help of this method. Classical decomposition models are used for short term forecasting
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