Fourier Series Analysis Of Seasonal Data:- Ekpenyong, Emmanuel J.

ABSTRACT

This study considered the application of Fourier Series Analysis in Modelling Seasonal Data and use of such model to forecast the future values of such data, hi order to achieve these objectives the data required for analysis and Regional Planning Department, University of Uyo. This set of data was the mean monthly temperature ofUyo Metropolis in Akwa Ibom Slate from 1998 to 2003. The model consisted of the Trend (T), the Seasonal or Detrended (D) and the I obtained as: Yt = 26.7 + 0.000736 t - 1.045Coscot - 0.601 Sinwt - 0.117Cos2wt + -0.183Cos3(ot 0.117Sin3wt + 0.250Cos4a)t + 0.1l5Sin4cot In testing for the significance ofthe parameters some parameters were found not to be significant; hence the model reduces to: Y( =26.7- 1.045 Coswt —0.601 Sincot + 0.462Sin2(at + 0.250Cos4cot In assessing the error component, it was found out that there existed some autocorrelation among its values and this led to the estimation of the error term by became negligible.  squares method. The general Fourier Scries model with the first two component was one to the term. Though the autoregressive 11 as time increases, the estimated error term 0.121Cos5cot + 0.034Sin5o?t +0.017Cos6o)t. error (Zt) components. Tire parameter estimates were obtained by ordinary' least interpretation were collected