改进的自适应Lasso方法在股票市场中的应用  

Application of Modified Adaptive Lasso Method in Stock Market

作　　者：王国长[1] 梁焙婷 王金枝 WANG Guo-chang;LIANG Bei-ting;WANG Jin-zhi(College of Economics, Jinan University, Guangdong Guangzhou 510632, China)

机构地区：[1]暨南大学经济学院统计学系

出　　处：《数理统计与管理》2019年第4期750-760,共11页Journal of Applied Statistics and Management

基　　金：函数数据变换模型及降维方法的研究(11501248)

摘　　要：在金融领域,自适应Lasso被广泛的用于股票价格预测模型中的变量选择和参数估计。然而,自适应Lasso是针对非时间序列模型提出的,忽略了时间序列模型特定的结构,比如时间序列模型中通常会出现滞后阶数越靠后,对未来的预测能力越弱的特性,从而,容易造成估计及预测不精确。因此,时间序列模型的变量选择惩罚参数的设计应与滞后阶数相关,即对越靠后的滞后阶数应加上越大的惩罚。为了充分考虑时间序列模型的特性且保留自适应Lasso的优点,本文针对时间序列AR(p)模型提出一种改进的自适应Lasso(MA Lasso)方法,通过在自适应Lasso惩罚基础上乘以一个关于滞后阶数单调不减的函数来达到目标。这样设计的惩罚参数的另一个优点是通过选取特定的惩罚参数,Lasso,自适应Lasso方法都是MA Lasso方法的特例。进一步,对于AR(p)模型中另一个重要参数p的选择问题,本文提出一种改进的BIC模型准则来选择p。最后,将MA Lasso方法应用到中证100指数中,实证分析表明,与Lasso和自适应Lasso相比,MA Lasso选择最简模型且预测效果最佳,即选择最少的预测变量的同时且具有最小的模型预测误差。In the financial field. Adaptive Lasso is widely used for variable selection and parameter estimation in stock price forecasting models. However, Adaptive Lasso is proposed for non-time series models, ignoring the specific structure of time series models. For example, in a time series model, the later the lag order is, the weaker the prediction ability for the future is. It is easy to cause the estimation and prediction to be inaccurate. Therefore, the design of the variable selection penalty parameter of the time series model should be related to the lag order, that is, the greater the penalty for the later lag order. In order to fully consider the characteristics of time series model and retain the advantages of Adaptive Lasso, this paper proposes a modified Adaptive Lasso (MA Lasso) method for time series AR(p) model, which achieves this goal by multiplying a monotone function on the lag order on the basis of Adaptive Lasso penalty. Another advantage of the penalty parameter designed in this way is that by selecting a specific penalty parameter, the Lasso and Adaptive Lasso methods are special cases of the MA Lasso method. Further, for the selection of another important parameter p in the AR(p) model, an modified BIC model criterion is proposed to select p. Finally, the MA Lasso method is applied to the CSI 100 index. The empirical analysis shows that compared with Lasso and Adaptive Lasso, MA Lasso chooses the simplest model and has the best prediction effect, that is, the least predictive variable is selected while having the smallest model prediction error.

关 键 词：Lasso 自适应Lasso AR(p) 股价预测 

分 类 号：O212[理学—概率论与数理统计]