The Adaptive LASSO With Improved Penalty Term And Applications Of In Time Series

With the rapid development of computer technology,the technology of automatic data collection has made rapid progress,and a large number of high dimensional data sets have been produced.Variable selection models,especially in high-dimensional data environments,have the advantage of selecting the optimal variables.Traditional statistical estimation methods,such as ordinary least squares(OLS),often perform poorly on high-dimensional problems.Therefore,the variable selection model led by LASSO comes into being.The LASSO method realizes variable selection and estimates the regression coefficients of each significant variable through the penalty likelihood method,and has been widely used in the environment of high-dimensional data.Later,more and more scholars innovated and improved the LASSO method and proposed many LASSO methods with good properties,among which the adaptive LASSO method was the most prominent.Adaptive LASSO aimed to improve the LASSO regression by introducing a weighting coefficient,and used adaptive weights to punish different parameters in the penalty function.In addition,adaptive LASSO also has the Oracle property that LASSO method does not have.It retains the advantage of original value LASSO estimation,and effectively corrects the estimation deviation of the model and speeds up the convergence rate.There is a lot of research on the properties of LASSO class methods in regression models,which has been widely studied and discussed,but the application of LASSO class methods in time series models is still in the early stage.And because adaptive LASSO is proposed for non-time series models,it ignores the special structure of the time series model and does not consider the sensitivity of the time series model to the time series,that is,the influence of the lagging order on the time series modeling,and with the increase of the lagged order period,the lag period has less and less influence on the current period.Therefore,time series data cannot be predicted well.On this basis,an improved method is proposed in this paper.On the basis of adaptive LASSO,it is divided by the intermediate term of the lag order,and gives relatively large penalty to the coefficient of the lag order greater than the intermediate term,and relatively small penalty to the coefficient of the lag order less than the intermediate term.The advantage of this improvement is that the compression of different coefficients can speed up automatic adjustment.Limiting the size of parameter space can reduce the complexity of the model and improve the convergence speed,so as to improve the accuracy and efficiency of variable selection and parameter estimation.In addition,through the feasibility analysis of theoretical property proof and data simulation,it is concluded that the improved method has Oracle property and excellent theoretical property.Then,the improved method is applied to the actual data of the unary autoregressive model for empirical analysis,and the comprehensive comparison with the existing mature methods is made to analyze the advantages of the improved method on the time series model.It is concluded that this method has good applicability in practice.On the basic,a multivariate ARIMAX time series model is established by using the daily closing price of the stock composite index as the explained variable.The adaptive LASSO method with improved penalty term is applied to the multivariate ARIMAX model for parameter estimation and variable selection,and the results are compared with the original ARIMAX model.