APPLICATION OF SPECTRAL ANALYSIS TO THE CYCLE REGRESSION ALGORITHM (TIME SERIES, FORECASTING, NON-LINEAR REGRESSION

Many techniques have been developed to analyze time series. Spectral analysis and cycle regression analysis represent two such techniques. This study combines these two powerful tools to produce two new algorithms; the spectral algorithm and the one-pass algorithm.;This research encompasses four objectives. The first objective is to link spectral analysis with cycle regression analysis to determine an initial estimate of the sinusoidal period. The second objective is to determine the best spectral window and truncation point combination to use with cycle regression for the initial estimate of the sinusoidal period. The third is to determine whether the new spectral algorithm performs better than the old T-value algorithm in estimating sinusoidal parameters. The fourth objective is to determine whether the one-pass algorithm can be used to estimate all significant harmonics simultaneously.;Based upon the analysis of the findings in this study, the following conclusions can be derived. (1) Spectral analysis is successfully linked with cycle regression analysis in this study. The results indicate that the spectral method of evaluating autocorrelations of the residuals, to obtain an initial estimate of a harmonic period, can replace the present T-value procedure. (2) The spectral algorithm was found to be extremely successful in estimating up to eight harmonics when it was linked with the combination of Tukey window and truncation point of 40% than with any other combination. (3) The new spectral algorithm performs better than the old T-value algorithm. As the number of harmonics were increased and as the percentage of the noise increased in the data, the spectral algorithm was found to perform better in estimating the harmonic parameters than the T-value algorithm. (4) The new one-pass algorithm fails to estimate all of the harmonics simultaneously when the periods of the two harmonics are close.;This study finds that the new spectral algorithm is a powerful tool in estimating time series components. The new algorithm can be used successfully in estimating one or more of the following time series components; linear and non-linear research indicates that there is a need to develop a technique to estimate all harmonics simultaneously.