An Improved Procedure for Fourier Regression Analysis

摘要

Fourier regression is a method used to represent time series by a set of elementary functions called basis. This work was used to propose a new procedure for Fourier regression which has the ability to reveal the period of significant frequencies and can be used to fit a periodic trend. The procedure involved the use of spectral analysis for component identification, discrete Fourier transform for estimating the coefficients and 95% confidence bound of the autocorrelation function for residual diagnostic check. The method was applied to Nigerian road accidental death time series data in order to test the efficiency. From the results, the spectral analysis magnitude plot revealed one and three components Fourier regression model. The periodic trend of one and three components Fourier regression model was fitted. The three components Fourier regression model was the most suitable and appropriate model since it has a close pattern to the original series and as well revealed the cyclical movement in Nigerian road accidental death. This was validated based on the three components residual autocorrelation function values which fell within the 95% confidence bound and this indicated the residuals are whiten. In conclusion, the proposed procedure for Fourier regression model was adequate for studying the important periodicities and their frequencies, fitting periodic trend and suitable for forecasting Nigerian road accidental death time series data.