Study Of The Theory & Methodology Of Interval-valued Symbolic Data Analysis With Application To Finance

Symbolic data analysis (SDA) is a new method analyzing and gleaning useful information from massive data. It is in such a way that summarizes large data to a dataset of a small size. One consequence of this is that the data may no longer be formatted as single values, but may be symbolic data. Interval number is a main type of symbolic data. This dissertation makes a study on the theory&methodology of interval-valued symbolic data analysis and its application in finance. The main points of this dissertation are as follows.1. Foundation of interval-valued symbolic data analysis Descriptive statistics for interval-valued symbolic data is mainly studied. Firstly, the empirical density function of interval-valued symbolic variable is defined. Based on this, methods of drawing the histogram and calculating of mean, variance, covariance and correlation functions for interval-valued symbolic variable are given. All of these become fundamentals for the next studies.2.Principal component analysis (PCA) for interval-valued symbolic data The two main methods of PCA for interval data are Vertices-PCA (V-PCA) and Centers-PCA (C-PCA). Comparative study is firstly made on them. Then a new method of PCA for interval -valued symbolic data called Common PCA from point view of common principal component. One advantage of this method is making dynamic PCA on time serial data. In order to make a further comparison on the three methods, an index which can indicate the goodness of fit of some method was defined by the Hausdorff distance. Then, comparative study of the three methods was made by means of simulation. Finally, an empirical research on Shanghai financial market is done by the given method. The relation between the risk and the company's scale and the dynamic evaluation on several stocks'behavior on the market are studied, respectively.3. Regression analysis for interval-valued symbolic data Firstly, estimation of regression parameters based on descriptive statistics for interval-valued symbolic data is given. On the other hand, for non-linear correlation data which can be linearized, a method of non-linear regression analysis for interval-valued symbolic data is put forward based on error transferring theory. Because of y|^_i and e_i are interval numbers, a type of rectangular residual plot is proposed to make regression diagnotics. Then, indices which can indicate the goodness of the model is defined based on the Hausdorff distance, that are called RMSE_H reflecting absolute error and U_H reflecting the relative error. Finally, it can empirical research on the correlation between CSI 300 and style indices of Chinese international trust & investment company (CITIC) is done by the given method.4. Solving of multi-objective linear programming with interval-valued symbolic coefficient Firstly, method of solving single-objective linear programming with interval-valued symbolic coefficient is discussed. Then, Zimmermann fuzzy method of solving of multi-objective linear programming with interval-valued symbolic coefficient is put forward. Finally, an empirical research on the portfolio investment is made.