State-dependent Model-based Nonlinear Time Series Modeling And Optimization Methods

Time series is an important tool to explore the motion law of real world. Examples of time series abound in the fields of engineering, economics, natural science and social science, which need to be furtherly processed and analysed. One fundamental task of time series analysis is the establishment of time sereies models. Traditionally, linear models have been widely used in practice assuming linear relationships among the series variables. Many real-world systems, however, are in general inherently nonlinear. In these cases, linear models are often inadequate to describe the complex actual systems. It is only over past several decades that various nonlinear time series models have been proposed. However, a tough problem arising in nonlinear models is the model parameter estimation. Nonlinear time series modeling and the optimization methods have become an important research area.This thesis considers modeling and predicting problem of two kinds of nonlinear time series. One is the nonlinear system whose dynamic behavior is regarded to change gradually as the "state variables (or working point)" varies continuously, such as the industrial processes, ecological systems. Aother kind of nonlinear system is the stochastic volatility financial processes. The main work and innovations of the thesis are summarized as follows.(1) Using a set of RBF networks to approximate the fuctional coefficients of state-dependent AR model, the RBF-AR model is obtained. This thesis investigates the modeling and forecasting problem for nonliear time series based on the RBF-AR model. The stability conditions of the RBF-AR are given. An efficient structured nonlinear parameter estimation method (SNPOM) is applied to estimate the model. Case studies on several benchmark time series show that the prediction performance of the RBF-AR model is superior to some other newly developed models.(2) The RBF-ARX model has been used sucessfully in nonlinear system modeling and control. In previous research and applications, the RBF networks used to approximate the state-dependent coefficients are always Gaussian function form. Howerver, this function may not always be optimal. The current study examines the variation in RBF-ARX model performance resulting from the use of six basis functions when applied to three benchmark time series, i. e. Mackey-Glass, Lorenz attractor and Box-Jenkins gas furnace time series. It is shown by the simulation tests that the optimal choice of basis fuction is problem dependent and evaluating all the recognised basis functions suitable for RBF-ARX model is advantageous.(3) We investigate nonlinear time series modeling by employing the radial basis function network with regression type weights (RBFRW) to approximate the functional coefficients of the general state-dependent autoregressive (SD-AR) model. The RBFRW differs from the conventional RBF network by the fact that its output weights connecting the hidden units to the output are linear combination of the input variables. The derived model (RBFRW-AR), which can be regarded as an enhanced version of previous RBF-AR model, is identified by a fast-converging estimation method via the structured nonlinear parameter optimization method (SNPOM). Case studies on various time series and chaotic systems show that the RBFRW-AR modeling approach exhibits much better prediction accuracy compared with some other existing methods.(4) The gradient-based algorithm SNPOM is a remarkable algorithm that can greatly accelerate the computational convergence of the parameter optimization process, however, lack a global perspective. A better procedure for estimation may be a combination of evolutionary algorithms and the SNPOM. Based on an evolutionary algorithm (EA) and a local search strategy——SNPOM, two hybrid parameter optimization algorithms for RBF neural networks are proposed. For automatic selection of the proper input variables, the number of hidden nodes of the radial basis function (RBF) network, and optimizing its parameters (centers and widths) simultaneously, a novel hybrid algorithm is proposed. In the proposed algorithm, the inputs, the number of hidden nodes and parameters of the RBF network are represented in one chromosome and evolved simultaneously by a genetic algorithm (GA). To improve the prediction accuracy of the RBF network and accelerate the convergence rate, a local search strategy based on the SNPOM is integrated into the GA. Experimental results show that the proposed approach produces parsimonious RBF networks, and obtains better prediction accuracy than some other algorithms.The RBF-AR(X) and RBFRW-AR model belong to a class of nonlinear model whose parameters can be divided into linear and nonlinear parts, and the number of linear parameters is much larger than that of nonlinear parameters. An off-line EA-SNPOM is developed to estimate the parameters of the RBF-AR(X) model and RBFRW-AR model. The results obtained from the simulation tests suggest that the combination of EA and SNPOM procedure further improves the modeling precision.(5) A hybrid constraint-hadiling method based on multiobjective optimization and adaptive penalty function is presented for constrained evolutionary optimization. The main idea of this approach is first to take advantage of multiobjective optimization techniques to extract the main information contained in the current population, and then further selcet the most valuable information by using the peanlty function to direct the population to evlove. By combining this constraint-handling technique with a model of a population-based algorithm-generator, a novel constrained optimization evolutionary algorithm is derived. Experiments on 13 benchmark test functions verify the effectiveness of the proposed method. The results show that the new approach is very robust and achieves very competitive performance with respect to some other state-of-the-art approaches. The proposed algorithm is also applied to estimate the RBF-AR model to obtain a staionary model with high prediction performance.(6) Financial markets generally display strong randomness, nonlinearity, jumps and especially stochastic volatility. We study the hidden excess demand and market liquidity behind financial market based on a discrete time microstructure model. An approach to the estimation of the model using evolutionary algorithm is presented to obtain the optimal architecture and the hidden excess demand and market liquidity processes. Based on the obtained excess demand information instead of the prediction of price, a simple asset allocation strategy is investigated. The threshold parameters are optimized by a constrained optimization evolutionary algorithm. Case studies on Cheung Kong and SZSE Composite Index from Hong Kong and Shenzhen stock market show that the filtered process of hidden excess demand is meaningful and efficient to be applied in an asset allocation strategy.