Application Of Chaos And Fuzzy Theories In Analysis Of Stock Data

With the development of science,the complexity of the world has gradually become the scientific research center.As the complexity of the object,nonlinear, symmetry properties and the fuzzy of boundary are incorporated into the areas of scientific research,science has entered a new stage of development.The new thinking associated with the complexity of scientific is developming,and the science of chaos and fuzzy theory is at the forefront.In this paper,chaos theory,fuzzy clustering theory,fuzzy pattern recognition and fuzzy comprehensive evaluation theory are used to study the data of the stock time series.The primary work in the paper as follows:In chapter 2,using the correlation dimension,the largest Lyapunov exponent and the Hurst exponent,it proves Shenzhen and Shanghai stock markets to be two chaotic systems based on the study of the nonlinear dynamical properities of the stock composite index sequence.In chapter 3,the specific data of 14 SMEs listed companies are used as demonstration to the fuzzy clustering.In the phase of selection in similar degree function,the included angle cosine and Hamming distance are used to study,and then a newly similar degree function "included angle cosine combined with Hamming distance" is constructed.Compared with the previous two on the basis of original data, it is approved that the result of the constructed method is more logical.In chapter 4,still taking the former 14 companies as an example,the indicator system for evaluation of investing value of the listed corporations is constructed,and the membership function of three categories of stock is given,and the weights method using factor analysis is used.In this chapter,beside the commonly model M(∧,∨),we still test other models:M(·,∨),M(∧,⊕),M(·,⊕)and M(·,+).Applying the five models,five results are obtained by using the fuzzy comprehensive evaluation method, thus the objective and reasonable basis for making decision is provided.