Regression Analysis Of Financial Time Series Based On Support Vector Machine

Nobel Laureate in Economics, Robert Merton considers that modern financial theory iscomposed of the time value of money, asset pricing and risk management. The core issue ishow to configure resources optimally under uncertain and Intertemporal environment. Basedon this understanding, R. Pliska extracted the random process and random control, two basicmodels from mathematical finance. Obviously, the former is the precondition and foundationfor the latter. Therefore, financial time series, a discrete stochastic process is the cornerstoneand key of the financial model. Because stock indices returns and volatility time series playan important role in investment portfolio and risk reduction, this thesis analyzes and modelsfor both.In this thesis, the main achievements include:1) Based on wavelet theory, a novel wavelet kernel (WK) is presented. Using high-dimensional mother wavelet function to generate wavelet frame directly through stretchingand translation we can gain a perfect base in Square integrable space and then constructwavelet kernel function satisfying the Mercer conditions. Theoretically the wavelet Kernelfunction can approximate arbitrarily to goal function in this space. The experiments showthat compared with Gaussian and other kernels, forecasting results by wavelet kernel canapproximate goal function closer.2) Based on manifold theory, a novel manifold wavelet kernel (MWK) is presented.Amari proposed a method modifying kernel function based on manifold geometry characterof data to enhance the performance of classification. This idea can be extended from classifi-cation to regression tasks by reducing the Riemannian metric around hyperplane.This modelhas the virtue of blending some data-dependent knowledge about support vectors into thekernel. The experiments show that manifold wavelet kernel can capture form of curve betterthan other kernels.3) Based on spline theory, a novel spline wavelet kernel (SWK) is presented. we first useone dimensional spline mother wavelet to construct one dimensional spline wavelet kernelby stretching and translation. And then, we continue to construct high dimensional splinewavelet kernel by multiplication principle. This kernel has the virtue of simple functional form and small supports. The experiments show that the capability of analyzing volatility ispowerful than other kernels.4) For financial time series'characteristics of dynamics, chaos and high noise, a novelwavelet support vector machine - dynamic model of stock (WSVM-DMS) is presented. Thismodel has virtues of small samples, good generalization, globally optimal solution and highnoise tolerance. Compared with other kernel functions in svm, all performance measures ofnew model based on its multi-scale property, are better in computer simulations and experi-ments on real world stock data.5) For volatility time series'characteristics of excess kurtosis, heavy tailedness andlong-range dependence, a novel wavelet support vector machine - generalized autoregressiveconditional heteroskedasticity (WSVM-GARCH) is presented. This model can capture thecluster feature of volatility well based on multi-scale analysis, which also has virtues of smallsamples, good generalization, globally optimal solution and high noise tolerance, too. Theapplicability and validity of new model are confirmed through computer simulations andexperiments on real world stock data.