Some Methods Of Variable Selection Comparing With Each Other In The Situation Of Defining Lags Of ARMA Models

The ARMA, one of models of time series, is widely used in finance, physics, biology and others fields. Especially the scholars in China Mainland showed the ARMA model can describe the one-step difference of the data of China Mainland CPI. So researching ARMA can acquire reasonable understanding about China economic. But we face a difficult problem that is how to choose the lags of AMRA. As the reason that the ACF and PACF of ARMA do not have the characteristic of truncation.The former solutions are choosing the variables by AIC,BIC and Mallow’s C methods and so on,.Though they can fit the time series model for the data in low dimensions, when we have the samples of high dimensions, they have their drawbacks. For example, the model will become very complex if the number of variables is large and the model that is made by methods we told above can be very unstable in high dimensions. So Tibshirani,R(1996) provided LASSO that based on Nonnegative garrote which is a method of selecting variables solve the problems. At the beginning of LASSO raised, it has been widely used in many spheres. But LASSO is applied to ARMA that is difficult as the result that algorithm of LASSO is LARS that its process of selecting variables is continuous that is different from the characteristic of ARMA. This essay introduced classic variable selective methods at the beginning, from the most intuitionistic and simple way that observing the graph of ACF and PACF to the considering the certified function such as AIC and BIC. At the same time, some non-parameter methods also are discussed that are widely used in the circumstances that the distributed function is indefinite, though the non-parameter methods are invalid in the high dimensions and large variables because of curse of dimensions. Then the writer will change the data to adjust to LASSO. But LASSO do not have the property of oracle, we introduce adaptive LASSO later. At the last of essay,the writer create a series of data based on ARMA(2,2),use some methods to define the lags and analyze the results.