Research On Fuzzy Time Series Model And Its Application In Trend Analysis Of Stock Exchange Composite Index

Fuzzy time series model provided a framework for dealing with problems with uncertainties that can not be handled by conventional time series analysis models. It has been researched more and more deeply and widely with the growing prediction of complex systems. In aspects of the theory and application of high forecasted accuracy and more reasonable semantic interpretation model, there are three hot issues for the researchers:constructing fuzzy logical relationship and fuzzy relation matrix, extracting fuzzy forecasting rules and improving the forecasted accuracy. Based on systematical analysis of domestic and international research results of fuzzy time series, the author has carried out research on the theory and application in forecasting and analyzing Shanghai Stock Exchange Composite Index and Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) in following aspects:(1) The thesis presents a method for constructing a weighted forecasting model on the basis of analysis of conventional fuzzy time series models. Since most of literatures proposed their models by displaying the process with some data sets, this thesis introduces mathematical forecasting formulas for the three conventional models to enhance their theory and apllication process. On the discussion of conventional models, it is clearly that the forecasting results just determined by the fuzzy set with the maximum membership degree which might not properly reflect the importance of other fuzzy relationships. To overcome this shortcoming, the thesis proposes a method for constructing weighted model and applies it to the three convetional models and type-2model. The improvements of the proposed models have been tested by experiments on Shanghai Stock Exchange Composite Index and university enrollment of Albama University.(2) To cope with the problem in the forecasting process with fuzzy relationships, the thesis presents three fuzzy time series models based on AFS theory, C-fuzzy decision trees and evidence theory, respectively. The first model obtains the fuzzy forecasting rules from AFS decision trees. The second model extracts the fuzzy rules with the aid of C-fuzzy decision trees which is improved by adding a splitting criterion and forecasting with KNN algorithem. The last model is constructed on the basis of evidence theory and improved by modifying the rule of belief functions combination which does not satisfy idempotence law. All of the three proposed models have been experimented on the Shanghai Stock Exchange Composite Index, the empirical results show that the models achieve higher forecasting accuracy than the conventional counterparts.(3) In the framework of fuzzy time series model, the thesis introduces the concepts of generalized fuzzy logical relationship and generalized fuzzy time series model. In conventional models, the forecasting results are determined by some fuzzy logical relationships, and the two adjacent fuzzy sets are assigned as the maximum membership degrees. The instability of the selection for fuzzy set is unreasonable for decisions and often results in low forecasting accuracy in the practical applications. To eliminate the deficiency mentioned above, the generalized fuzzy relationship and model are then introduced in this thesis. These new concepts can satisfy the need of theory and practice for the reason that the the generalized fuzzy logical relationship comprised of the secondary fuzzy logical relationships as well as the principal fuzzy logical relationships, which are the conventional fuzzy logical relationships. Furthermore, this thesis also presents a method for constructing generalized fuzzy time series model and higher order generalized fuzzy time series model on some operations proposed for fusing the information of fuzzy logical relationships in different hierarchies. All of these models have been tested by above three data sets, and the empirical results show that the proposed models outperform the conventional counterparts.Finally, Chapter6draws the conclusion on the researches and discusses about the further study.