Cycle regression analysis: Simultaneous estimation of trigonometric components of a time series

Cycle regression analysis is a continuously evolving family of algorithms that provides the simultaneous estimation of all parameters of a sinusoidal model. The newest members of the family, which add spectral analysis to the nonlinear regression methodology, are introduced in this paper. The new algorithms have been applied to some of the most classic time-series data sets in the literature. A comparison of the results of the analysis are made to the results of applying two other forecasting techniques: stepwise estimation procedure and asymptotic maximum likelihood approach. The ability of the cycle regression analysis method to simultaneously estimate parameters is shown to provide an inherent advantage over these other two techniques. A set of contemporary business data from the M-2 competition is also analyzed using cycle regression analysis and the results presented. One of these new cycle regression analysis algorithms was selected to be included among the forecasting techniques used in the international M-2 competition.