Nonlinear Filtering Algorithms And Applications In Neural Network And Financial Market Modeling

With the rapid development of science and technology, nonlinear filtering methods have gained extensive research and application in signal processing, target recognition, system identification, parameter estimation and economic statistics, and so on. Traditional nonlinear filtering methods are implemented based on linearization and Gaussian noise condtions, which may reduce the filtering precision. Particle filter, which is formulated as a common state filtering and parameter estimation method for nonlinear non-Gaussian time-varying system, has some unique advantages. But the particle degeneracy, sample depletion and other issues have been plaguing its the development and applications. The thesis focuses on a further study on particle filter with the choice of importance density function.This paper mainly studied nonlinear filtering methods and their applications in neural network and financial microstructure modeling. Because the statistical characteristics of the process noise directly affects the parameter estimation precision and the convergence speed, some improvements have been done for overcoming these shortages of the traditional neural network training algorithms based on nonlinear filtering methods. Also, to correctly and thoroughly capture the typical nonlinear, non-Gaussian and volatility characteristics in financial market, some extended market microstructure models were introduced. And nonlinear filtering methods were used to estimate states and parameters of the extended models by empirical research. The main research works and achievements are summarized as follows.Firstly, nonlinear filtering algorithms are systematically investigated under a unified framework of Bayesian sequential estimation theory. To relieve the degradation problem of the particle filter, an improved particle filter, APF-IEKF (auxiliary particle filter with iterated extended Kalman filter), is proposed, which consists of an auxiliary particle filter that uses an iterated extended Kalman filter to generate the importance proposal distribution. When the new algorithm calculates the proposed probability density distribution, the sampling particles can utilize the system current measures. So that gets the particles distribution more approach to the station posterior distribution. The experimental results also illustrate the improved particle filter is superior to the standard particle filter and the other filters such as PF-EKF (particle filter with extend Kalman filter), PF-UKF (particle filter with unscented Kalman filter) and APF-EKF (auxiliary particle filter with extended Kalman filter), and it has less running time. Additionally, the performance on these algorithms is compared and reasons for the improvement of various nonlinear filtering methods and application range are analyzed.Secondly, the thesis solves the difficulties in expanding the nonlinear filtering algorithms into neural network parameter estimation from two aspects. On the one hand, because of low filtering accuracy and divergence caused by unknown system noise statistics in neural network state space model, an adaptive process noise covariance particle filter (APNCPF) is proposed. Combining the particle filter, the novel algorithm can estimate sequentially the covariance of unknown system noise online. On the other hand, a self-organizing state space (SOSS) model is built, which involves forming augmented state vectors consisting of all the unknown parameters and the outputs. The single, joint state vector not only reveals all the relevant information on the future output contained within the past input, but also completely characterize the system dynamic characteristics. Moreover, the two methods are applied to multi-layer perceptron (MLP) and RBF training. Experimental results verified their effectiveness.Thirdly, SNPOM (structured nonlinear parameter optimization method), as a gradient-based algorithm, is a remarkable algorithm to RBF-AR model that can greatly accelerate the computational convergence of the parameter optimization process. To further enhance its learning precision and especially process sample data with great noise, RBF-AR model, as an extended radial basis function neural network, is transformed into the state space model. Compared with the traditional three-layer RBF network, the novel extended RBF network has an additional linear output weight layer. The EM (expectation maxmization) algorithm, incorporated with EKF, is used to estimate the parameters and the unknown noise covariances of stochastic dynamic system. It is shown by the simulation tests that our method for the reconstructive RBF-AR network provides better results than SNPOM, especially in low SNR (signal noise ratio).Finally, aiming at modeling the dynamic characteristics of financial market, and considering the huge price fluctuations caused by the market uncertainty, the existence of leverage and the characteristics of higher kurtosis and thicker tail, some extended market microstructure models were proposed, such as jump market microstructure model with nonhomogeneous possion process, market microstructure model with leverage effect and market microstructure model with heavy-tailed t distribution. Some theoretical explanations to leverage effect and heavey tail are provided. A new nonparametric method proposed by Lee was used to detect time-vary ing jump intensity. Based on the detection of jump, its parameters are estimated by a method combined UKF (unscented Kalman filter) with maximum likelihood method. Because of inter-emporal negative correlation and non-Gauss, Markov chain Monte Carlo (MCMC) algorithm procedures are designed for parameters estimation of leverage effect market microstructure model and heavy-tailed market microstructure model. Simulation results show the effectiveness of the above methods. The empirical results in Chinese stock market and the United States stock market show that the two stock markets have higher kurtosis, thicker tail and leverage effects. The jump frequency of stock market in China is obviously higher than that in the United States. DIC (deviance information criterion) is used to compare the heavy-tailed market microstructure model with the market microstructure model based on a normal distribution and it is proved that the former is superior to characterizing the leptokurtic of stock returns in stock market.