Multivariate Ar (p) Model Estimation Theory

This dissertation deals with how to estimate parameters of a model of multivariable weak stable Auto-regression Equation on time series ( marked by AR(p) ) and formulizes properties of them. It comes up with a new notion, d-solution, which is applied to the distance estimation, by virtue of Hilbert space; furthermore, the dissertation has gained a necessary condition which is identity of minimum mean-square value in linear function classes, so that d-solution extends minimum mean-square value within the domain of nonlinear function equation or equation system; and, the dissertation studies in detail the classical moment estimation and maximal likelihood estimation on the parameters of AR(p) , a series of theorems in the estimation section shows the moment estimators are consistent on the ground of large samples Jikewise, those distribution functions of the estimated parameters accord to maximum likelihood estimation converge Gauss distribution if the white noise is Gaussan. A important result is the one-order expression of AR(p) Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR(p) is only a certain more-multivariable power series processAnd, if a process is described as an AR(p), the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one. Simplification of AR(p) not only brings about orthogonal F(h) but also provides global foretelling formula.