混频数据抽样模型等权低频化处理的估计偏误研究

Research on Estimation Bias of Low Frequency Conversion Equally-weighted for Mixed Frequency Data Sampling Model

文章通过剖析三种基础形式的混频数据抽样模型的内部结构,将其分解为等权重加权平均和非等权重加权平均两部分之和,从理论上证明了将高频数据等权低频化处理的EQW模型会造成高频变量的信息损失。并通过数理推导,证明了EQW模型的普通最小二乘估计量（OLS）有偏,而且高频解释变量与低频被解释变量的频率倍差越大,估计量的有效性越低。

This paper analyzes the internal structure of the three basic mixing frequency data sampling model（MIDAS）, and decomposes the structure into the sum of equal weight and unequal weight. And then the paper theoretically proves that the EQW model with high frequency data converted to low frequency data will cause information loss of high frequency variables. Finally by mathematical deduction, the paper demonstrates the bias of the ordinary least squares（OLS） estimation of the EQW, and that the greater the difference-in-difference of the high frequency explaining variable and low frequency explained variable, the lower the effectiveness of the estimator.