相依条件下部分函数线性回归模型估计方法研究  

Estimation of Partial Functional Linear Regression Model under Dependent Condition

作　　者：李气芳 苏梽芳[2] LI Qifang;SU Zhifang(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,363000,China;School of Economics and Finance,Huaqiao University,Quanzhou,362021,China)

机构地区：[1]闽南师范大学数学与统计学院,漳州363000 [2]华侨大学经济与金融学院,泉州362021

出　　处：《应用概率统计》2022年第6期904-918,共15页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11871259);福建省创新战略研究项目(批准号:2021R0153);福建省社会科学基金项目(批准号:FJ2021C027);闽南师范大学高级别培育项目(批准号:MSGJB2021023)资助。

摘　　要：部分函数线性回归模型是指因变量为标量、自变量包含标量和函数型变量的混合数据回归模型.现有的部分函数线性回归模型估计方法,假设函数型变量服从独立同分布,这与金融等领域函数型时间序列数据的相依特征不符.本文首先针对具有相依特征的函数型数据提出两种数据驱动的函数主成分表示方法,然后对模型中的回归系数函数进行正则化表示,最后把部分函数线性回归模型的估计转化为多元线性回归模型的估计.蒙特卡洛模拟结果表明,文中所提方法的参数估计误差较小、样本外预测精度较高;实例分析也表明文中所提方法在股票预测上的有效性.Partial functional linear regression model refers to a type of regression machine that contains mixed functional and numerical data at the input and numerical data at the output.In the existing partial function linear regression machine estimation algorithm,it is assumed that functional data sample follow independent and identical distribution,which is inconsistent with the dependent characteristics of functional data in the financial and other fields.Therefore,the article first proposes two data-driven functional principal components representation methods for function data,then the regression coefficient function is regularized,and finally the estimation of the partial functional linear regression machine is transformed into the estimation of the multiple linear regression machine.The Monte Carlo simulation results show that the methods proposed in this paper have smaller parameter estimation errors and higher out-of-sample prediction accuracy when dealing with dependent data,the case analysis also shows the effectiveness in stock forecasting.

关 键 词：部分函数线性回归模型 相依函数型数据 长期协方差函数 残差协方差函数 

分 类 号：O212.4[理学—概率论与数理统计] F224.0[理学—数学]