Research On Nonlinear And Non-Gaussian Time Series Prediction

Decision is a basic practical activity in manufacture, life and work. Whether an individual or a country will be faced with making decision, that is to say, he must choose the optimum alternative from various scenarios in many cases. Forecast is the premise of decision and any successful decision can not be separated from the scientific forecast. Therefore, forecast is also a basic activity.For decades, time series prediction is an important research aspect in forecast field, which is theoretically important as well as practically urgent in many scopes. This dissertation focuses on the time series prediction. And the study is carried out in the following aspects:1. In order to cope with the nonlinear and non-Gaussian time series, a RBF-HMM model, which is based on radial basis function (RBF) neural network with the assumption of measurement noise being hidden Markov model (HMM), is proposed in this dissertation. At the same time, we come to conclusions as follows: (1) The assumption of measurement noise being Gaussian process is only a special case of that being HMM, whereas the assumption of measurement noise being HMM is an extensive form; (2) Once the HMM has one hidden state which follows Gaussian distribution, the RBF-HMM model will degenerate into a nonlinear autoregressive moving average (NAMAR) model with Gaussian white noise; (3) When the HMM has one hidden state which is Gaussian distribution and the RBF neural network has no hidden neurons, the RBF-HMM model will degenerate into an autoregressive moving average (AMAR) model with Gaussian white noise;2. Within the above framework of time series forecast, time series prediction based on static RBF-HMM model is studied. At first, parameter estimation of RBF network is discussed, then methods for selecting the number of input nodes and hidden neurons are introduced respectively, and an algorithm of parameter estimation based on gradient descent is proposed; Secondly, we introduce the methods for selecting the number of hidden states, the number of Gaussian mixture models and its parameters; At last, an algorithm of time series prediction based on static RBF-HMM model is developed and corresponding experimental research is done. 3. In order to overcome the shortcomings that static RBF-HMM model can't describe time series dynamically, a dynamic RBF-HMM model is proposed. Firstly, measurement equation and state evolution equation of dynamic RBF-HMM model are put forward; Secondly, Rao-Blackwellised particle filter is introduced in detail; Thirdly, sequential Monte Carlo (SMC) method is used to estimate parameters and predict time series on-line in the dynamic RBF-HMM model; At last, both the data of smoothed monthly mean sunspot numbers and the data of weekly passengers in Nanjing Lukou international airport are analyzed, and experimental results indicate that dynamic RBF-HMM model is effective.4. A dynamic RBF-HMM model with variable structure, whose structures and parameters vary with time, is presented. At first, some parameters are adjusted once the structures of RBF neural network and HMM change; Then SMC method is used for on-line estimation of the structures and parameters and time series on-line prediction, an corresponding algorithm is developed subsequently; At last, both the data of smoothed monthly mean sunspot numbers and the data of weekly passengers in Nanjing Lukou international airport are analyzed, and experimental results demonstrate that the dynamic RBF-HMM model with variable structure is effective.5. Multistep-ahead time series prediction based on RBF-HMM model is analyzed. The basic concept of multistep-ahead prediction is introduced and forecasting steps are given at first; Subsequently, multistep-ahead time series prediction based on RBF-HMM model with SMC method is studied and a corresponding algorithm is developed; At last, the data of CRUspi are analyzed, and experimental results show that the proposed model is effective.6. In order to predict the real price of shipping steel, a dynamic RBF-HMM model with variable structure is applied, and experimental results indicate that the model is effective. Moreover, the management information system (MIS) for price prediction of shipping steel has been established.