The Analysis And Research Of Predicting Technology For Financial Time Series Based On Nonlinear Dynamics

Financial market is the essential economic system of a country, financial time series is a primary data type in the application of financial area. Analyzing predicting and controlling of such kind of data is the basic work of the economic and financial activity. Financial time series is composed of bond profit, foreign exchange rate, stock price, futures price, etc. In this paper, financial time series is chosen to be studied by using nonlinear time analysis method of nonlinear dynamics; both univariate and multivariate data are investigated. The dissertation consists of the following contents:Firstly, the primary developing procedure of financial time series analysis method is introduced, and explains why this research topic is chosen. The history and newly improvements of nonlinear dynamics technology and the method of time series analysis are reviewed, and the latest developing progress of these research areas and their combination are illuminated, too. The necessary procedure of nonlinear time series analysis is composed of noninearity test, determinism test, the choic of parameters of reconstructed phase space, compute nonlinear invariant. The influence of noise is concerned and analyzed. Then, various methods related to nonlinear time series analysis are discussed, such as univariate time series'phase space reconstruction, noise level estimation and reduction, the prediction of nonlinear time series, etc. In order to describe the quality of the reconstructed phase space, several important nonlinear invariants are introduced. Secondly, the necessarily of nonlinearity and determinism examination of a time series is explained, and two primary methods: BDS and surrogate are introduced. Four stock market's index time series are investigated after stationary dealing. Recurrent plot is introduced and used to do the determinism examination. Considering the particularity of financial time series, a calendar corrected surrogate method is explained with computer simulation.Then, basing on the above studying result, the complex system of four investigated stock market is reconstructed. The method of choosing the optimal minimal dimension of reconstructed phase space is analyzed, and its shortcomings have been pointed out, the way to overcome this bug is introduced. Further, the influence of noise when we try to reconstruct phase space with noisy data is studied, which will show that it is unmeaning if we do not reduce the noise. After reducing the noise of stock index series, the complex systems of these stock markets are reconstructed and compared with the prior one.After this, some popular nonlinear time series predicting methods are analyzed. Based on local method, several predicting estimators are defined, such as kernel regression method, local weighed linear method and RBF method. Clear and noisy Lorenz data are used to test the predicting estimator, the test result show that these estimators are robust enough to deal with nonlinear time series. Then these estimators are used to predict with financial time series. According to particularity of financial time series, two improved methods based on local method...