Research Into Modeling And Forecasting Of Financial Data Based On Multi-Dimensional Taylor Network And Its Extension

The financial system is the dominant and pivot of market mechanisms for rational allocation of resources in the market economy, and the normal operation of the financial system is the necessary condition to ensure the stability of the national economy. Financial data, including stock price, deposit and loan, fund, insurance and foreign exchange, is the most important data type of economic data. Research, analysis and prediction of financial data can contribute to the formulation of national macro-control guidelines. The main approach to studying financial system is to build its mathematical model. Existing models based on financial system operating mechanisms are mainly for concrete financial sectors for the purpose of solving concrete problems, but are limited by the complexity and volatility of the financial system. The method of data modeling, which is based on non-mechanism, can process a large amount of financial data rapidly through high-speed operation of the computer, and hence is more widely used in the analysis of financial data. However, it has the disadvantages of focusing on the internal relations of data only and divorcing from reality. In order to create a better financial model, which helps lay a foundation for the study of economic control and national macro-control, a method based on multi-dimensional Taylor network (MTN) for modeling and forecasting of financial data is proposed. Furthermore, the extended methods based on dynamics cluster MTN (DCMTN), intermittent feedback MTN (IFB-MTN) and multiple MTN with intermittent feedback (MIMTN) are proposed.In this dissertation, based on the modeling of financial system data, a number of mathematical models and corresponding solution algorithms are developed in accordance with different focus of modeling. The main tasks of the dissertation are summarized as follows:1. A data-based financial system dynamics model is presented to address the problem that the financial system contains massive internal factors and has complicated structures. The form of the general dynamic model is studied first, and then the multi-dimensional Taylor network model is proposed by combining the characteristics of financial system with multi-dimensional state vectors and the basic principles of Taylor expansion. The rationality of the multi-dimensional Taylor network model expression is proved. The order of weighted term arrangement and its recursive expression are defined. The general method for parameter identification of the multi-dimensional Taylor network model is obtained by the conjugate gradient method for iterative solution of the model parameters. In order to test the validity of the model, firstly the impact of random disturbances on the financial data is reduced through data filtering and decomposition methods, and then the multi-dimensional Taylor network model is established for each decomposed data sub-sets, whose parameters are identified and predicted, finally the prediction result is output by superimposition. The simulation results show the effectiveness of the model and the algorithms, and also lay the foundation for the expansion studies based on multi-dimensional Taylor network model.2. A financial system dynamics forecasting model which can change the dynamic characteristics by different predicted targets is proposed to develop the problem of fast internal liquidity, variable structure and characteristics in the financial system. After the study of the financial system dynamic features, the dynamics characteristics are defined, and the rationality of its mathematical expression is proved. Depending on the different degree of similarity between data points of financial data, the specific form of the dynamics similarity is defined, and its properties are summarized and proved. Combining the multi-dimensional Taylor network and dynamics similarity, the financial system dynamics forecasting model based on dynamics cluster multi-dimensional Taylor network is developed. The parameters of the model are identified by the least squares estimation method. Test results demonstrate that the model of dynamics cluster multi-dimensional Taylor network is feasible and effective.3. According to the fluctuation characteristics of the financial system on account of herd behavior, a data-based financial system dynamics model with the mechanism analysis as auxiliary is formulated. The mechanism of herding and its causes are studied, and its form of fluctuations which is externally represented through data is analyzed and summarized. Then the concept of intermittent feedback is given, and the specific mathematical expression of intermittent feedback is described by the superimposition of dead zone functions with beginning and ending thresholds in the positive and negative directions. The feasibility of using intermittent feedback to describe the system control states is demonstrated. Combining the multi-dimensional Taylor network and intermittent feedback, the financial system dynamics model based on the intermittent feedback multi-dimensional Taylor network and its parameters identification method are proposed. The feasibility of intermittent feedback multi-dimensional Taylor network model is verified by application examples of modeling the actual financial data. The prediction results validate that it is superior to traditional non-mechanism data model.4. To deal with the targeted imprecise problem in system identification of the intermittent feedback multi-dimensional Taylor network model between the intermittent feedback part which simulates herding and the multi-dimensional Taylor network part, an optimization model based on alternating iteration of parameters is developed. In order to balance the two sub-modules of the intermittent feedback multi-dimensional Taylor network dynamic model, the multiple multi-dimensional Taylor network (MMTN) model structure is constructed, through the characteristics mining from the multi-dimensional Taylor network. It is proved that the multiple multi-dimensional Taylor network can be applied to modeling superposition of data sub-sets by the same state vectors, different target outputs. According to the multiple superposition property of multiple multi-dimensional Taylor network, and combining the intermittent feedback multi-dimensional Taylor network model, the financial system dynamics model based on the multiple multi-dimensional Taylor networks with intermittent feedback is developed. The specific method of parameters identification is given. The example results are provided to illustrate that the prediction effect of proposed modeling method is better than the traditional non-mechanism modeling method, or intermittent feedback multi-dimensional Taylor network modeling method.