Theoretical Study And Empirical Analysis On Fractal Structure Of Shanghai Stock Market

Efficient Market Hypothesis (EMH) is a prerequisite theory of analyzing the capital market all the time, as one of the foundations stone of economics of Neoclassicism. EMH is also the core of the theory of quantified financial market. Financial theory models, such as Modern Portfolio Theory (MPT), Capital Assets Pricing Model (CAPM), Arbitrage Pricing Theory (APT), are set up on the foundation of EMH and have built investment theory system in modern times. But EMH is incapable of explaining lots of abnormal phenomena of finance market because of its assumptions being not in compliance with the facts in finance market, moreover, capital market theory based on EMH has been oppugned and challenged at some extent. Fractal Market Hypothesis (FMH) has changed people's knowledge of the statistical property of finance market, and has better explained the phenomena in finance market. Therefore fractal market theory would affect the analysis and study of problems in finance market. There is very important significance to capital pricing, risk management, market supervising and price forecasting.This paper proceeds from the EMH, proposes its defects, draws into FMH. We introduce the theory content of FMH, course and application of rescaled range analysis (R/S analysis), approach of Hurst index, and then use this theory to analyze the stock market of Shanghai. We find that the Shanghai stock market presents leptokurtic and fat tails, which does not follow normal distribution, but has a more oblivious fractal structure. It presents strong persistence, all of Hurst index we have estimated are more than 0.5; it has a non-periodic cycle and a strong self-similarity.The fractal structure of stock market is a frontier-complex question of the modern financial domain. The innovation of this paper mainly lies in: After studying the excellence of domestic production and foreign production about fractal market, we propose a defect in the course of R/S analysis and improve it. We use the improved R/S analysis to empirically analyze the stock market of Shanghai, and bring forward the program of S-plus for the approach of Hurst index. We compositively use significance test, confusion test, modified R/S analysis to prove the conclusion of classical R/S analysis. Moreover, the samples of this paper include a long period and a big range, not only divides the composite index of Shanghai stock market into three periods, but also has a non-linear test of the five sorted index of Shanghai stock market initially.