The Application Study Of Bayesian LASSO On The Stationary Time Series

With the accumulation of the massive high-dimensional data on the economic and financial aspects, modeling and analysis has become increasingly important. Generally, in the face of the same data, the researchers may have many choices of models available. So, how to choose an appropriate model has become an important focus of theoretical and empirical world. Before1980, statisticians are more concentrated in the direction of the information criteria, such as AIC, BIC and Cp criteria. Although their principle is simple, but they require high computing needs, when the variables get more, if we want to select the model that meet specific criteria smallest, such methods may face the difficulty of the actual operation. Therefore, one research methods that can greatly reduce the times of searches and have some theoretical advantages began to be raised, Tibshirani (1996) proposed Least Absolute Shrinkage and Selection Operation(LASSO) method can greatly avoid the instability under the conditions of high-dimensional by least squares method, and it also can automatically compress the non-significant parameters to zero. Efron (2004) proposed the small angle regression (Lars) algorithm has been one of the most popular method to solve the LASSO problem.For the reason that LASSO method is equivalent to the Bayesian posterior estimate of the Laplace prior distribution, so Bayesian LASSO method (Park2008) was formally proposed and applied gradually. It not only can select the model, but also can play the advantages of Bayesian statistics and can be approached using MCMC method parameter estimation. There are three basic methods:AR model, ARMA model and ARCH models for stationary time series. Even time series model using LASSO method has been researched, however the attempts to explore the Bayesian LASSO methods of stationary time series models in research applications were almost none. Based on this theoretical and practical background, this paper attempted the application study of Bayesian LASSO method to stationary time series model.First, this paper reviewed the existing basic methods and research results about time series, lasso and Bayesian lasso. Second the paper described the LASSO, Bayesian basic principle and the Bayesian LASSO approach. And the third, this paper introduced the three basic stationary time series models:AR, ARMA and ARCH model, we successfully applied the Bayesian LASSO into these models by handling data transformation. Fourthly, we carried out data simulation through the R software platform. Finally, we conducted an empirical research taking SSE300Index for example.The main conclusions of this paper include:First, stationary time series model can be estimated using Bayesian LASSO effectively but not always better than LASSO. Second, Bayesian LASSO method can provide more information on the probability of decision-making.