Some Research About The Methods Of The Estimation And Prediction Of Multivariate MA (q) Models

In this dissertation, the methods of prediction and parameters' estimation based on stationary multivariate moving average models (MA(q)) are studied systematically. Some properties of these methods are formulized.First of all, this dissertation deals with asymptotic properties about the estimation for the mean vector and correlation matrix function of a stationary multivariate time series. These asymptotic properties play a role in describing independence of multivariate time series and building models by them.Furthermore, with using some orthogonal-projection theories in a Hilbert space, it introduces some properties of best linear predictor defined in inner-product space, which are the basis for the next work.Then, it uses the innovations algorithm in the multivariate MA(q) models and comes up with the formulas about one-step and h-step timely recursive prediction of multivariate MA(q) models, after it particularly studies the recursive prediction of time series. These formulas would be able to enhance obviously the efficiency of prediction.Finally, sample innovations Z|^_k is a series of error, whenX₁,X₂,...,X_k-1 are used to predict X_k .In contrast with Z|^_k, the theoreticalinnovations Z_k is made, while one utilizes all the historical datato predict. Often, sample innovations could not properly approximate the theoretical one (especially fork =1,2,...,q). The number of the historical data X₁,X₂,...,X_n should be increased gradually, until the differencebetween Z|^_k and Z_k ( k=1,2,...,n ) could be ignored. When sampleinnovations properly close to theoretical one, the innovations recursive algorithm is used to estimate the parameters of multivariateMA(q)process and the estimation formula is introduced.