摘要
含有L_q罚函数的线性回归可以进行变量选择或者系数缩减,利用Lq罚函数的这种性质,可将H-P滤波和L_1趋势滤波推广为L_q规则化趋势滤波。在内在趋势是分段线性趋势(0<q≤1)和无折点趋势(q>1)两种假设下,使用LLA方法和凸优化技术进行估计,提出修正的GCV准则进行调整参数选择。数值分析显示,在不同的假设下,本文提出的方法优于H-P滤波和L_1趋势滤波。该方法可以有效地提取时间序列的内在趋势,也可以扩展得到其他形式的解,在时间序列分析中有重要的意义。
Penalized linear regression with Lq penalty can select variables or constraint coefficients. This paper makes use of the propertie of Lq penalty to extend H-P trend filtering and L1 trend filtering to Lq trend filtering. We research on two different assumption for underlying trend, which are piecewise linear trend when 0〈q≤1 and trend without knots when q〉1. We estimate them through LLA meth- od and convex optimization and also propose a modified GCV criterion for choosing the tuning parameter. The numerical analysis shows that, under different assump- tion, our method performs better than H-P trend filtering and 1.1 trend filte- ring. This method can extract the underlying trend efficiently and can be easily modified to adapt to other assumptions, thus it is of great significance in the time series analysis.
出处
《数量经济技术经济研究》
CSSCI
北大核心
2014年第5期151-160,F0003,共11页
Journal of Quantitative & Technological Economics
