Two Types Of Stochastic Model Of The Limit Theory Related To The Unit Circle

The theory of unit root in the macro economics, finance, econometrics, and other fields occupy the important position. With the constant improvement of unit root theory, when multiple time series are considered, it may be useful to allow simultaneously for various types of behavior in the individual series. The research about mixed roots theory at home and abroad is also growing. This paper studies two types of stochastic model of the limit theory related to the unit circle. First, on the basis of the Phillips & Ji Hyung Lee’s article(2012), we establish a new VAR(1) model,, We main study the limit theory of regression estimator Rn. The model expands the results of Phillips and Lee (2012). This model provides a theory of unit root test results.In addition, We consider special sequences of random variables{Xn,n ∈ Z}, whose probability generating functions Pn(z)=∑κn=0ZκP(Xn= Κ) are polynomials of degree n, all of whose roots lie on the unit circle. The nature of the random variable sequence has an in-depth discussion In Hsien-Kuei and Vytas’s article, and conclusion is given that random variables converges to a certain random variable X in distribution. We further study the convergence speed of the random variable sequence and get moderate deviation...