周期特征下序列的非参数估计及实际应用  

Nonparametric Estimation of Periodic Characteristic Sequences and Its Practical Application

作　　者：李小亮 李朝柱 汤美微 LI Xiao-liang;LI Chao-zhu;TANGMei-wei(Jiyang College of Zhejiang A&F University,Zhuji 311800,China;School of Economics and Management,Huzhou College,Huzhou 313000,China;School of Economics,Nanjing University of Finance&Economics,Nanjing 210023,China)

机构地区：[1]浙江农林大学暨阳学院,浙江诸暨311800 [2]湖州学院经济管理学院,浙江湖州313000 [3]南京财经大学经济学院,江苏南京210023

出　　处：《数理统计与管理》2024年第3期395-406,共12页Journal of Applied Statistics and Management

基　　金：国家社会科学基金青年项目(19CTJ011);浙江省哲学社会科学规划项目(20NDQN327YB);浙江省教育厅一般项目(Y202145961)。

摘　　要：考虑周期长度未知的时间序列,建立含趋势项和周期项的非参数模型。首先采用带惩罚的回归残差和判定周期长度,再基于Profile最小二乘法和局部线性逼近得到趋势函数和周期序列的估计。讨论了估计量的渐近性质,包括周期长度估计的相合性以及周期序列和趋势估计的渐近正态性。数值模拟呈现了本文方法在提高模型可解释性等方面的优点。最后将本文方法分别用于城市二氧化碳浓度以及城市PM2.5浓度数据的拟合,展示了它们的实用性。Considering the time series with unknown period length,a nonparametric model with trend term and period term is established.Firstly,the period length is determined by the regression residual with penalty,and then the trend function and period sequence are estimated based on profile least square method and local linear approximation.The asymptotic properties of estimators are discussed,including the consistency of periodic length estimation and the asymptotic normality of periodic sequence and trend estimation.Numerical simulation shows the advantages of this method in improving the interpretability of the model.Finally,our method is applied to urban carbon dioxide concentration and urban PM2.5.The fitting of concentration data shows the practicability of this method.

关 键 词：周期长度 光滑趋势 周期序列 识别条件 Profile最小二乘 

分 类 号：O212[理学—概率论与数理统计] O212.7[理学—数学]