R-Matrix Analysis of Structures in Economic Indices: from Nuclear Reactions to High-Frequency Trading

Abstract

It is shown that the R-matrix theory of nuclear reactions is a viable mathematical theory for the description of the fine, intermediate and gross structure observed in the time-dependence of economic indices in general, and the daily Dow Jones Industrial Average in particular. A Lorentzian approximation to R-matrix theory is used to analyze the complex structures observed in the Dow Jones Industrial Average on a typical trading day. Resonant structures in excited nuclei are characterized by the values of their fundamental strength function, (average total width of the states)/(average spacing between adjacent states). Here, values of the ratios (average lifetime of individual states of a given component of the daily Dow Jones Industrial Average)/(average interval between the adjacent states) are determined. The ratios for the observed fine and intermediate structure of the index are found to be essentially constant throughout the trading day. These quantitative findings are characteristic of the highly statistical nature of many-body, strongly interacting systems, typified by daily trading. It is therefore proposed that the values of these ratios, determined in the first hour-or-so of trading, be used to provide valuable information concerning the likely performance of the fine and intermediate components of the index for the remainder of the trading day.