A Study On Fractal Structure In Chinese Stock Market--Theoretical & Empirical Discussion

Until now, people have being zealously explored the behavior of capital market, and have advanced a series of theories, including random walk theory (RWT), efficient market theory (EMT), behavior finance theory (BFT), fractal market theory (FMT) and so on. Efficient market theory is incapable of explaining lots of abnormal phenomena of finance market because of its assumptions being not according with the facts in finance market, moreover, Capital market theory based on efficient market theory have being at some extent oppugned and challenged. However, Having broken through the assumptions , that is, entirely rational investors, independence, linearity, normality, etc, fractal market theory have changed people's knowledge of the statistical property of finance market, and have 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.Fractal is a set which part is similar to totality, and it shows the properties of self-similarity, scaling-invariant, fractal dimension, part random and certain totality. Stock return series is a typical random time fractal. There are three aspects to understand the fractal structure of stock market, that is, from geometry, Stock return series presents fractal dimension, complex structure, self-similarity; From market, there are many investors who have different investment term; from statistics, stock price series is characteristic of long memory and fractal distribution, moreover its statistical dependencies of returns have similar form for various time increments.This study use fractal theory and several statistical methods to discuss the fractal structure in Chinese stock market. After the introduction of fractal theory and methods, there are a lot of empirical analyses. We not only study monofractal structure and multifractal structure of stock market, but also use ARFIMA and FIGARCH to model long memory, furthermore to a certain extent modify the traditional capital market theory. Monofractal process is a long-term statistical behavior and has the same fractal character at different time or at locality. After non-linear testing, we employ classical R/S, modified R/S, fractal dimension, fractal distribution to empirically analyze Chinese stock market. ARFIMA model could describe short-term memory and long-term memory for mean series, but FIGARCH could those of variance series. Further we discuss scaling function, local Holder index, generalized Hurst index and multifractal spectrum to analyze Chinese multifractal structure. Multifractal model of the stock return have also been discussed.We conclude that Chinese stock market has distinct fractal structure and is a typical fractal market. Chinese stock market presents leptokurtic and fat tails, it does not follow normal distribution but fractal distribution. Chinese stock market presents strong persistence, almost all of Hurst index we have estimated are more than 0.5; it has a non-periodic cycle and a strong self-similarity between different time increments and between various stock indexes. The results of empirical study indicate that long memory models such as ARFIMA-FIGARCH indeed are better than traditional series models. Parts of different times and different volatile ranges represent multi-fractality.Although there are several innovative studies and many heuristic conclusions, because of short time and my limited knowledge, there are many problems which need study furthermore in my paper.