函数系数协整模型局部线性估计方法的改进  

Improvement of Local Linear Estimation Method for Functional Coefficient Cointegration Model

作　　者：曹晓舟 Cao Xiaozhou(School of Mathematical Sciences,University of Jinan,Jinan 250002,China)

机构地区：[1]济南大学数学科学学院,济南250002

出　　处：《统计与决策》2023年第21期23-28,共6页Statistics & Decision

摘　　要：函数系数协整模型可以克服非参数建模时的“维数困难”,同时体现系数的动态变化,被广泛应用于非平稳数据间复杂问题的研究。实践中经济序列常表现出时变波动方差和厚尾特征,传统核权最小二乘估计方法将不再适用。鉴于此,文章基于L1损失函数重构估计流程,选择表现稳健的局部线性核估计方法,并引入自适应方法,提出局部线性自适应最小绝对离差估计(ALADE)。模拟结果验证了所提估计方法可提升系数估计精度,优化模型整体拟合效果,同时绝对值交叉验证方法在选取最优窗宽时优势明显。实证分析发现,所提方法可识别中英两国汇率和价差间的动态协整关系,拟合系数平滑且接近理论值。Functional coefficient cointegration model can effectively overcome the“Curse of Dimensionality”in nonparamet-ric modeling and reflect the dynamic change of the coefficients,so it is widely used in the study of complex problems between non-stationary data.In practice,economic series often exhibit time-varying volatility and heavy-tailed characteristics,so conven-tional kernel weighted least squares(KLS)estimator is no longer applicable.In view of this,this paper constructs the estimation process based on L1 loss function,then selects the robust local linear kernel estimation,and introduces the adaptive estimation method.Finally,the paper proposes the Local Linear Adaptive Least Absolute Deviations Estimation(ALADE).The simulation re-sults verify that the proposed estimation method can improve the accuracy of coefficient estimation and optimize the overall fitting effect of the model,and that at the same time,the absolute value cross validation(ACV)method has obvious advantages in select-ing the optimal bandwidth.The empirical analysis shows that this method can identify the dynamic cointegration relationship be-tween the exchange rate and differences in price between China and the UK,and that the fitting coefficient is smooth and close to the theoretical value.

关 键 词：函数系数协整模型 局部线性ALADE 时变波动方差 厚尾特征 

分 类 号：O212.7[理学—概率论与数理统计]