季节虚假回归中参数及统计量的分布特征

实际应用中,通常在回归模型中添加季节虚拟变量来消除季节性的影响,但是当数据生成过程是独立的季节单位根情形下会导致虚假回归现象的发生.本文利用泛函中心极限定理推导出回归参数及相关统计量的渐近分布,从理论上解释了季节虚假回归问题产生的根源.并且,采用蒙特卡罗方法模拟了回归参数及相关统计量的分布特征.最后,通过与非季节情形进行了比较,发现此时R2和DW统计量不再能有效识别普通最小二乘回归中的“季节虚假回归”现象.

Characters of coefficients and statistics in seasonal spurious regression

In practice,seasonal dummies is used in regression to remove seasonality in economical time series.When data generation process is independent seasonal unit roots,the relation between variables may lend to spurious.In this paper,we deduce the limit distribution of regression coefficient and correspondence statistics,such as t,R~2,DW,etc,by functional central limit theorem and interprete the result of seasonal spurious regression issue in theory.By Monte Carlo simulation method,we get the distribution characters of regression coefficients and correspondence statistics.Compared with non-seasonal situations,we discover that R~2 and DW can not efficiently detect seasonal spurious regression phenomena in OLS.