Nonlinear Detection And Reconstruction Of Multivariate Financial Time Series

The financial system is an open complex system, and there are intricate relationships among the economic variables. From "Random walk theory (RW)" and "Efficient Market Hypothesis (EMH)" to "Capital Asset Pricing Model (CAPM)", theories about financial market have emerged in an endless stream. However, traditional researches are generally based on the linear framework. There is a lot of evidence showing that linear methods can't give efficient explanation of the complex financial market volatility. Since the 1980s, an increasing number of finance scholars have been exploring and looking for some nonlinear methods to explain financial phenomenon and forecast the price evolvement in financial market. Financial market research in the nonlinear framework has very important theoretical and practical significance.In this thesis, multivariate financial time series are analyzed and forecasting based on the theory of chaos and support vector machines. The thesis mainly includes the following integrations.The representative detection methods of chaos in univariate financial time series and multivariate financial time series are introduced in this thesis. Then, each method's characteristics and shortcomings are discussed. The improved algorithms of some methods are also proposed in this thesis.Influence of noise on the largest Lyapunov exponent of multivariate chaotic time series contaminated with noise are analyzed with the improved algorithms proposed in this thesis. Numerical results are given mainly for Ikeda map, Henon map, Lorenz map and Chen map. The time series used here are produced by a superposition of Gauss white noise series generated by random number and noise-free series. Changes in the trend of the largest Lyapunov exponent under different signal-to-noise ratio (SNR) are studied.Multivariate nonlinear prediction methods based on the concept of phase space reconstruction is proposed. Stock price time series are forecasted with these methods. The results indicate that multivariate nonlinear prediction model outperforms univariate nonlinear prediction model.At last, a novel forecasting model of multivariate financial time series based on chaos theory and least squared support vector machine (LS-SVM) is proposed. The experiment on the prediction of the specific financial series is carried out. The results indicate that LS-SVM prediction model of multivariate time series outperforms LS-SVM prediction model of univariate time series.Considering the nonlinear characteristics of financial market, the theories of chaos and support vector machines are applied to multivariate financial time series analysis. The results show these theories and methods can explain and forecast the fluctuation of financial market. The research has very important theory and practice sense for nonlinear modeling and forecasting of financial time series.