均值波动率回归（英文）

MEAN VOLATILITY REGRESSIONS

在无风险资产和有风险证券的离散时间资产定价问题中,常用包含相关的随机成分和非随机成分的增量过程模型来表示.受此启发,文章提出了一类融合了非随机和随机成分的半参数回归模型.与经典的回归模型不同,在此模型中均值回归函数包含了方差部分,并且模型变量与某个状态变量有关联,因此模型更具有特定的经济意义.文中的一个例子解释了GARCH-M模型与现有的广义漂移模型不能包含本文中所提出的模型.文章还表明,虽然增量过程只是两个部分的加权和,但模型的统计推断不能够简单地通过两个独立系统来完成.文章研究了估计量的渐近理论性质,并通过蒙特卡洛模拟考察了估计量的小样本性质.最后利用中国金融年鉴2004-2005的数据分析了中国金融市场的财富增量过程.

Motivated by increment process modeling for two correlated random and non-random systems from a discrete-time asset pricing with both risk free asset and risky security,we propose a class of semiparametric regressions for a combination of a non-random and a random system.Unlike classical regressions,mean regression functions in the new model contain variance components and the model variables are related to a state variable,for which certain economic interpretation can be made.A motivating example explains why a GARCH-M and existing general diffusion models cannot cover the proposed models.Further,we show that statistical inference for the increment process cannot be simply dealt with via two separate systems although the increment process is a weighted sum of the two systems.We further investigate the asymptotics of the estimators.Monte Carlo simulations are conducted to examine finite-sample performance,and a real dataset published in Almanac of China＇s Finance and Banking（2004 and 2005） is analyzed for illustration about the increment process of wealth in financial market of China from 2003 to 2004.