Pseudo-Additive (Mixed) Fourier Series Model of Time Series

This study improves on the Additive Fourier Series and traditional model of discrete periodic time series. It seeks to formulate a mixed (multiplicative-additive) Fourier Series model which decomposes a time series into multiplicative trend, seasonal components and additive error component together with additive trend. It is discovered that for time series with strongly marked and obviously fluctuating seasonal effects a multiplicative-additive (mixed) Fourier series model is suitable. The relevance of the new model is shown by analyzing the rainfall data of Uyo metropolis with the use of the model. The resulting model gives Yt = 210.1 (1-0.984 cos ωt) which fits well to the original data and can be used in forecasting future values of the rainfall data.