Fourier series models through transformation

Abstract

This study considers the application of Fourier series analysis (FSA) to seasonal time series data. The ultimate objective of the study is to construct an FSA model that can lead to reliable forecast. Specifically, the study evaluates data for the assumptions of time series analysis; applies the necessary transformation to the data and fits multiplicative and additive FSA models. In order to meet the aforementioned objectives of the study, the average monthly temperature data (1996 – 2005) collected from the National Root Crops Research Institute, Umudike are subjected to statistical analysis. The preliminary analysis of the data makes transformation necessary. As a result, the square transformation which outperforms the others is adopted. Consequently, each of the multiplicative and additive FSA models fitted to the transformed data are then subjected to a test for white noise based on spectral analysis. The result of this test shows that only the multiplicative model is adequate. Hence, it used to make forecast of the future values of the original data.