Isotonic Regression And Cointegration In Finance Fields

Statistical inference under order restrictions in an important area of statistical analysis plays a key role in this field. In the 60's, Statistical inference under order restrictions is attached importance to us. Statistical inference is a active topic and we convene conference of nations. Moreover, the studies of isotonic regression and cointegration are very important in this field.The application background of the isotonic regression is quite profuse, and that, an important method of computing isotonic regression is PAVA algorithm. Theoretic researches on isotonic regression become mature day by day. It is widely and will be more widely used. For programming with isotonic regression, there have been many excellent research works concerned. One of the content of the research is that we transform general distribution into asymptotic distribution, and estimate the mean of general distribution with the restricted EM algorithm and generalized PAVA algorithm. The convergence of the EM algorithm is given.Considering that research works on isotonic regression are relatively mature, the present work expands into cases under cointegration restrictions. There exist cointegration in a lot of finance models. For example, there is consume and payout model. There shows a unit root in consume and payout, but in a long time, the ratio of consume and payout is constant. The another example is a purchasing power equal theories. The other of the content of the research is that a vector process is considered. The difference of order 1 of the vector process is a vector autoregressive (VAR) and there exist cointegration restrictions in the components of the VAR process. Maximum likelihood estimates of the parameters are given. There are three steps in this work. First, account regressive selecting Ordinarily Least Square regressive is calculated. Second, the representative correlation coefficients are calculated. Third, Maximum likelihood estimates of the parameters are calculated. By dint of Ordinarily Least Squares regressive is a pivotal step. The researches of cointegrations are prodigious practical meaning in finance fields.