Research On The Interactional Multivariate Regression And Multivariate Time Series Mixed Model

The time series analysis with multiple equations is an important part of time series analysis, which is widely applied in the field of macro-economics and draws more and more attention in the world. In practice, we may get different fitting and predicting results for different model and adopt different modeling approach and parameter estimation. A perfect model is not only simple but also has preferable fitted and predicted results. Meanwhile, the parameters estimated have excellent statistic properties. This paper does some researches on the time series analysis of multiple equations to get better results in theory and practical application.Firstly, we improve interactional multivariate regression and multivariate time series model, the VAR model and the time series simultaneous system model to present a new model. The improved model considers not only the relation between certain dependent variables and present value of other ones but also the relation between it and lagged value of all dependent variables. The new model still considers that between present value and lagged value of some external variables, which is more reasonable.Secondly, the methods of selecting lagged rank of model and interpretive variables of each equation are investigated. We adopt AIC or BIC to obtain the lagged rank and step-wise regression to choose the interpretive variables of equations, which makes new model simple and useful.Thirdly, the methods of estimating parameters of model are researched in detail. This paper proposes three new methods. The first is the full information maximum likelihood method with linear constraint of coefficient matrixes in structure equation. Under certain condition the calculation formula of parameters estimation is obtained. The second is the amendatory indirect generalized ridge estimates of the parameters. This paper not only educes its calculation expression but also proves that statistic properties of parameters estimated are excellent. Meanwhile, the method of selecting ridge parameters is given. The third is the ill-condition separation algorithm in multicollinear regression model. This paper gives the process in detail and proves that the asymptotic statistic properties of parameters estimated are excellent.Finally, this paper takes some macroeconomic variables for example to validate the rationality of new model and draws a conclusion that the fitted and predicted results of model are exact and efficient.