Spectral estimation and time-series extrapolation of prime indicators of society

Abstract

In an effort to determine the cyclic patterns present in the prime indicators of society, Haustein and Neuwirth [3] applied Discrete Fourier Transforms (DFT) to the differences between the logarithmic transformed actual data and selected exponential trend lines. In this paper it is argued that standard DFT analysis is inappropriate for these time series, as is the multiple curve-fitting exercise used to isolate the trends in the data. Instead, the spectral analysis has been redone using a method recently developed by the authors that is appropriate to such limited time-series data. It can detect a periodic signal even if only part of a cycle of that signal is contained within the time-series data. The method also provides an estimation of the time series outside of the original data limits. In addition, single logistic trends are used, and each data set is more carefully screened to ensure approximate stationarity. It is shown that spectral analysis in any form should not be applied to innovation and invention data. Most importantly, the cyclic variations present in world primary energy consumption are also present in world industrial production; this confirms their strong interrelationship. Only the primary energy consumption data series shows stationarity, however, a result that implies a development over time independent of other variables. These two observations suggest that industrial production could be determined from the primary energy consumption, a result that is in direct contrast to the causality generally assumed in an econometric approach to energy forecasting.