The Limit Theory Of Two Types Of Unit Root Process

The theory of unit root occupies the important position in the field of econometrics, since White(1958)and Dickey & Fuller(1979,1981)deduced the limit theory of unit root process,asymptotic distribution propertis of unit root process became one of the core problems in the field of econometrics. This paper studies the two kinds of unit root model,on the basis of Phillips&Lee(2012),we choose a vector autoregressive model of non-stationary,Yt=RnYt-1+μt,t=1,2,...,n, Phillips & Lee regarded Pn as 1+c/n,c is an arbitraty finite constant,θn=1+b/κn,6>0.In this paper,we regard Pn as 1-hn/n,hâ†'0,that is to say,Pn=1-hn/n is faster than Pn=1+c/ntend to 1, and θn remain the same,in this case,we study the limit theory of regression estimator Rn. The asymptotic properties of this model provide a theory of unit root test results. In order to distinguish the mildly,explosive behavior induced by θn from the very nearly unity induced by pn,statistical tests need to differentiate θn from Pn as nâ†'+∞.Another kind is on the basis of the research on the Anderson(1959),the model xt= αXt-1+μt,t=1,…,n,α>1,{ut,t≥1)is continuous and independent identically, distributed random variables,and E(μt)=μ,V(μt)=σ2.Anderson(1959)regarded αas unknown pa-ameters,proved the estimator of α is consistent estimate of α by the method of moment generating function.We regarded & and μas unknown parameters,prove the estimators of a and μare consistent estimalte of α and μ by a different method,and deduce the limit distribution of estimators.