Research On The Permutation Entropy And Efficiency In Shanghai Stock Market

Modern financial theory is established on the basis of efficient market hypothesis.Scholars developed a lot of important financial model based on it too. But financialmarkets become complex adaptive systems because of "limited rationality" investorswho participate in. Complexity makes it more difficulty for people to understand andcontrol the financial markets on the one hand and it supports the financial system’srelative stability on the other hand. Therefore, considering whether there is interactioninfluence between the complexity of financial market and its effectiveness, and whatform is possible influence in become valuable research topics and contents.Entropy is a concept of thermodynamics in the beginning, which is used todescribe the chaos degree of a thermodynamic system. In the field of economics,entropy represents the uniform and uncertain degree in a complex system, so it can beused to measure complexity degree of a system. In addition, the fractal markethypothesis, which is put forward to amend the shortage of the efficient markethypothesis in recent years, played an important role in the analysis of financial marketvalidity. Therefore, Use entropy and effectiveness index as indexes of marketcomplexity and effective respectively, make the closing price from July15,1991toJune29,2012of Shanghai composite index the research object, which is classified toseven time interval according to its characteristics, the following aspects on thementioned problems above are studied.First of all, create a validity index to represent the market validity with theabsolute deviation of Hurst index and0.5, and make an empirical research on theShanghai stock market efficiency with multifractal detrended fluctuation analysis. Theresults show that, the Shanghai stock market is far from "weak form" effective state.Secondly, discuss the complexity of Shanghai stock market with permutationentropy theory. The empirical analysis shows that permutation entropy, which reflectsthe order of share price change, can extract characteristics of all sorts of share pricechange period quickly and efficiently, thus it can reaction stock market’s complexitydegree correctly.Finally, analyze correlation between the Shanghai stock market efficiency andpermutation entropy combined with "sliding window" technique. Application of BDStest shows that there are nonlinear relations between efficiency index and permutation entropy. Using of cross correlation coefficient analysis shows that it exists the crossinfluence between them and long-term effect is more significant than short-term one.Nonlinear Granger test put forward by Diks et al points out that there is very soundlytwo-way Granger causality between market efficiency index and permutation entropy.Therefore, short-term market complexity increases may reduce the marketefficiency, but in the long run, increasing the market complexity improves theefficiency of the stock market. This article confirmed Liu’s view, namely marketefficiency and the complexity of the market itself closely related from the perspectiveof empirical research.