Buys-Ballot Estimates Of The Trend Curve And Seasonal Indices For Additive Model When Trend-Cycle Component Is Cubic

ABSTRACT

The Buys-Ballot estimation procedure developed by Iwueze and Nwogu (2004) for time series decomposition when trend-cycle component is linear and was later extended to cases where trendcycle component is quadratic by Iwueze and Ohakwe (2004) is been proposed to cubic trend-cycle component. The two alternative methods (the Chain Base Estimate and Fixed Base Estimate) were considered and estimates were derived for the additive model. Simulated examples were used to illustrate the methods developed. Nigerian Stock Exchange Market Capitalization (N' Billion) data for the period of 1985-1994 and Quarterly Gross Domestic Product at Current Basic Prices (N' Billion) for Other Transport Services data for the period of 1981-1992 were analyzed to further illustrate the application of the proposed method in a real life time series data. The Buys-Ballot estimates (CBE and FBE) were compared with Least Squares estimates and the Chain Base Estimate were found to perform better in terms of forecasts. The modified Diebold-Mariano test were further used to test for equality of the forecast accuracy of the three models considered and the results revealed a significant difference among the three fined models