Elucidation of Chaotic Market Hypothesis Based on Ergodic Theory

Abstract

We develop a method of directly testifying the efficient market hypothesis (EMH) proposed by Fama by using the ergodic theory to connect microscopic price fluctuations with macroscopic behavior. After testing the validity of the method by using exactly solvable chaos, we found a novel periodic structure in the 5-min chart data of the Nikkei averages in 2019 with our developed new correlation function based on the characteristic function. This directly denies the EMH. Statistical data of the empirical studies have shown that a stable law well describes the price fluctuations of financial markets as predicted by the most generalized version of the central limit theorem called the universal super generalized central limit theorem (USGCLT) we discovered recently. The concept and proof of the extension of the super generalized central limit theorem (SGCLT) is also given to illustrate the mechanism of universality such that a sum of random numbers with nonidentical power law distributions converges to a stable law in distribution. With these theoretical facts together with the empirical fact of the data denying the EMH, we propose the chaotic market hypothesis (CMH) based on the ergodic theory to capture the essential characteristics of the financial markets.