Some Applications Of Lasso Method In Time Series

In this paper, we studied some applications of Lasso method in time series. In recent years, people pay more and more attentions to how to use mathematical statistical models to dig out the useful information from a large number of data. In the initial stage of modeling, if some important independent variables are missing, the model tends to produce deviation, so people will choose as many variables as possible. However, the modeling process needs to find the independent variable set which have strong explanatory power for the dependent variable. The Lasso method is a kind of estimation method which can simplify the index set, and it can improve the explanatory power of the model and the accuracy of the prediction. Therefore, using the Lasso method to select variables can reduce the bias in the modeling.The change point is the time point of sudden change of the sample distribution or the numerical characteristic. The change point problem is one of the hot issues in statistics, econometrics and other subjects. The research of change point detection is also widely applied to many fields. The Lasso method can also deal with the estimation problem of change point. The change point estimation of Lasso method is equivalent to the variable selection problem after transform. Then, using the method of variable selection to deal with the problem, it can get good estimation results.The main work of this paper is as follows:1. In the first part, we studied the application of Lasso method in the selection of variables. The Lasso method and Adaptive Lasso method are compared in time series in this part. The simulation results indicate that the Adaptive Lasso is more effective than the Lasso method. By using these two methods for variable selection in the HS300 index of the historical data, the results show that the two methods can select variable effectively and accurately, but parameters of Adaptive Lasso method are more accurately. Forecast results according to the selected variables and their parameters also show that the variable selection and parameter estimation of the Adaptive Lasso method are effective.2. In the second part, we studied the application of Lasso method in change point detection. In this part we first compare the change point estimation of Lasso method and Adaptive Lasso method in the numerical simulation. The estimation result is accurate. Then, using the closing price of HS300 for change point estimation, the results are good.