SELECTING AN ADEQUATE MODEL FOR TIME SERIES DECOMPOSITION WHEN THE TREND CURVE IS QUADRATIC

Abstract

The Buys-Ballot (B-B) approach for the decomposition of additive and multiplicative models in descriptive time series (TS) was examined in this paper. The selection of an adequate model is very important as it shows the underlying structure of the series because the fitted model will be used for future forecasting. Mis-specifying the model characteristics of the data is consequential and can result in biased tests and false predictions The Buys-Ballot method was demonstrated for the selection of an appropriate model and a statistical test that will aid in the selection between additive and multiplicative models was proposed when the trending curve is quadratic. The model identified was used for the forecast. Using the B-B technique, the column variances for the additive model do not contain the seasonal effect while that of the multiplicative model contains the seasonal effect. This distinction was then applied to select between additive and multiplicative models. The chi-square test was proposed for the selection between additive and multiplicative models for the decomposition of TS data. The results when applied to a quadratic trend curve reveal that the appropriate model for the decomposition of the data is the additive model as all calculated chi-square values are within the chi-square acceptance region based on a two-tail test at a 1% level of significance. The additive model identified was then used to decompose the series and the trend analysis model was used for the forecast of the series. The chi-square test was proposed to justify the Buys-Ballot method for...