Seasonal Modelling of Fourier Series with Linear Trend

Abstract

This work was motivated by the need to model a periodic time series function with linear trend. A Fourier series representation with detrended linear function was proposed. In this representation, the time series  is expressed as a combination of the linear trend component and a linear combination of  orthogonal trigonometric functions; where  is the number of seasons. The method was applied to a rainfall data and the proposed model was found to give a good fit. Comparative study was carried out with the complete Fourier representation. Diagnostic checks revealed that the proposed method performs better the pure Fourier approach.