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Analyses of Statistical Structures in Economic Indices

The complex, time-dependent statistical structures observed in the Dow Jones Industrial Average on a typical trading day are modeled with Lorentzian functions. The resonant-like structures are characterized by the values of the basic ratio: the average lifetime of the individual states associated with a given structural form divided by the average interval between adjacent states. Values of the ratio are determined for three structural forms characterized by the average intervals: 50 to 100 seconds (the fine structure), approximately10 minutes, and approximately1 hour (the intermediate structures I and II). During the trading day the values of the basic ratio associated with the fine structure of the index are found to lie in the narrow range from 0.49 to 0.52. This finding is characteristic of the highly statistical nature of many-body systems typified by daily trading. It is therefore proposed that the value of this ratio, determined in the first hour-or-so on a given day, be used to provide information concerning the likely performance of the fine, statistical component of the index for the remainder of the trading day. For the intermediate structures the basic ratios are approximately 0.6 and therefore they too can be analyzed as individual states. Keywords: Analytical economics; Lorentzian analyses of statistical structures in the Dow Jones Industrial Average; basic parameters of economic indices.