A new methodology for the logistic analysis of evolutionary S-shaped processes: Application to historical time series and forecasting

A new multi-logistic methodology to analyze long range time series of evolutionary S-shaped processes is presented. It conceptually innovates over the traditional logistic approach. The ansatz includes computing the residuals to an optimized multi-logistic trend curve least squares fitted to the time-series data. The elements of the residuals series are checked for autocorrelations and once detected the residuals series is further analyzed to search for eventual presence of underlying periodic structures using a truncated Fourier sine series. The method foundations ensures both a universal applicability and a capacity to disclose the existence of active clocks that can be possibly traced to the driving motors of the evolutionary character of the time series, due to the responsiveness of corresponding process to the development of economic cycles. On associating these two views, it is found that the methodology has a strong potential to improve the quality of short-term forecasts. These findings have been put to test through applications of the methodology to studying the time evolution of two commodities of strong economic and social importance (corn and steel) and good results were consistently obtained for both the analytical and forecasting aspects.