The Comparative Research On Fractal Structure Of Stock Markets

Efficient Market Hypothesis is the base of modern finance theory. Many financial models are proposed based on EMH. With this formulation, many scholars have made empirical investigations on EMH, but a lot of researches conclude that the EMH is not satisfied with the reality. The finance markets are highly complex, irregular, so Fractal Market Hypothesis was proposed. EMH is a special of FMH, so it can be used to test the market's efficiency.There are a lot of problems in China's stock markets, so the China's stock market is not efficient. Some of the researches have confirmed this point. Based on these researches, this paper applies a new method called R/S analysis to test the efficiency of stock markets.This paper focuses on the comparative research on the fractal structure of stock markets by using R/S analysis. Firstly, Kolmogorov-Smirnov test method was used to test the normal distribution of indices, including DJI, S&P500, FTSE, N225, SSEC and SZCI, we find that the returns of these indices are not normal distribution. Then, the R/S analysis is utilized to research the efficiency of these stock markets. We find that the China's stock market has a more oblivious fractal structure, and drew a conclusion that China's stock markets are not efficient. Then we established a stochastic volatility estimation model with ITO process, and use the model to estimate the volatility of returns of China's stock markets. The methodology used to test the long-term memory of the volatility is Hurst's R/S analysis. The result shows that the returns' volatility has long-term memory and clustering.At last, this paper analyses the factors which affect the market efficiency, and proposes some advises.