Extant methods for identifying longer‐term cycles in economic and social time series are in various ways limited. Spectral analysis assumes stationarity of variance and reasonably consistent periodicity, while moving average methods are susceptible to judgmental bias and other artifacts. This paper explores the use of stepwise polynomial regression analysis as a method for deciding, on statistical grounds, whether a longer‐term cycle exists; and for characterizing its specific form. Used with U.S. economic and social data, the polynomial regression analysis provides evidence for the existence of two longer‐terms values corresponding to the Juglar cycle and the Kuznets cycle; no evidence for a “long wave”; Kondratieff cycle is found. The cross‐series findings also suggest that variations in war and war preparedness play a role in generating such cyclic effects.