The Methods Of Estimation And Prediction Of Multidimensional AR(p) Models

In this dissertation , the methods of prediction and parameters' estimation based on stationary multivariate autoregressive models (AR(p)) are studied systematically. Some properties of these methods are formulized.In the first part, it introduce some basal conceptions about multidimensional stationary time series, contained the estimation and property of mean vector and auto-covariance function. Then the stable condition of multidimensional AR(p) models are discussed.In the second part, the four methods of estimation for multidimensional AR(p) models are researched. First, by reference of estimation methods in one-dimensional AR(p) model and based on the eauqtion of Yule-Walker in literature [9], it obtain the recursive estimates. Second, it improve the traditional LS estimates, thus, it will be more easily calculated by program in MATLAB. After that, it obtain the durbin-levinson recursive estimates based on the durbin-levinson algorithm in literature [9]. Finally, Based on the assumption of Gauss white noise, it construct the log-likelihood function for the existing observations, and then, the maximum likelihood estimation of parameter's array and white noise covariance matrix are discussed.In the third part, quoting the traditional theory in linear prediction, it obtain the forecasting of multi-dimensional AR(p) model. Then, it riefly introduce the criterion of order determination for AR(p) model.