Criterion and Measurement of Complexity of Stock Market: From Chaos, Fractal to Complexity Degree

The research of how to quantitatively depict the complexity, nonlinearity of stock market is now in the ascendant. The criterion methods, which could not comparably measure the complexity degree, have been generally adopted for the depiction research on stock market complexity up to now. The analysis of the complexity characteristic of stock market was deepened through introducing characteristic quantities of complexity (such as Lempel-Ziv complexity, statistical complexity & approximate entropy) and combining them with the criterion methods of chaos & fractal. The Lyapunov exponent, correlation dimension and the above three characteristic quantities of complexity of 5 stock markets were calculated. By virtue of the results, the conclusions are as follows: i) The Lyapunov exponent and correlation dimension, which could only be regarded as criterion indexes of complexity of stock market, could not be further used to compare the complexity degrees when the stock markets are in the same state, i.e. chaos or non-chaos; ii) the results of statistical complexity and approximate entropy accord with the conclusions from Lyapunov exponent and correlation dimension; iii) some characteristic quantities of complexity measure, such as statistical complexity and approximate entropy, could cover the shortage of complexity criterion methods to comparably measure the complexity degree of stock market.