Estimate And Predictor For State Space Models With Time-Varying Matrix

State space is a sort of model structure which has a wide range of including various statistics models. Owing to given some model hypothesis under this structure, it can be producted corresponding Kalman filter and their smoother system which can apply to almost aspects of model inference such as parameter estimate,model diagnose and predictor. Accordingly, there are great advantages of inference to state space models. Concretely, what I worked conclude the following aspects:First, based on the mature theory of central linear Gausssian state space models which have invariable. coefficient, I discuss parameter estimate, diagnose and predictor for linear Gausssian state space models with noncentre and time - varying matrix by their Kalman filter and smoother, and the maximum likelihood estimations of parameter under various hypothesis are concentratly studied especially.Second, the recurion rules of exact initialisation filter and augmented filter and corresponding smoother in the situation of diffuse initialization are stuied. As an application, I give the mode of maximum likelihood estimation for regression models which have exogenous explanatory variables that coefficient matrix vary with time by the exact initialisation of filter and augmented filter and corresponding smoother in the hypothesis of diffuse initialization, forcast about observational variable of identified model by exact initialisation of Kalman filter is revealed simultaneously.Third, as to Non - Gaussian and Non - nonlinear state space models, linearisation, extended Kalman filter and smoother, maximum likelihood estimation are chiefly stuied. At the same time, analysis from both classical and Bayesian standpoint on exact estimation of stocked state vestor fuction by simulating based on importance sampling are researched, and by this simulating, we can obtain the estimate both of ikelihood fuction and forecast for observational variable.Fourth, In view of linearization is core segment of inference on Non - Gaussian and Non - nonlinear state space models based on their approximating models, I work on three sorts of Non - Gaussian models with time - varying matrix, and show the concrete linear models produced by EM algorithm. It is the three sorts of models that conclude major common Non - Gaussian state space models.Fifth, approximating linearizational models of the most mediocre Non - nonlinear state space models based on first order Taylor series and EM algorithm are also researched in this thesis. As an application, I dispose of the SVM model which can expose interemporal relations between stock index returns and volatility, and give the mode of maximum likelihood estimation for SVM model, moreover, forcast about observational variable of identified SVM model by extended Kalman filter is also given together.