我使用以下模型运行SAS回归:
ods output ParameterEstimates=stock_params;
proc reg data=REG_DATA;
by SYMBOL DATE;
model RETURN_SEC = market_premium;
run;
ods output close;
其中RETURN_SEC是每秒股票的回报率,而market_premium是SPY指数的回报减去无风险利率(无风险利率非常接近零,因为它处于第二级别)。
然而,我在market_premium系数中获得了大量的0(不是全部,但有很多)。当我检查日志时,它说:
NOTE: Model is not full rank. Least-squares solutions for the parameters are
not unique. Some statistics will be misleading. A reported DF of 0 or B
means that the estimate is biased.
NOTE: The following parameters have been set to 0, since the variables are a
linear combination of other variables as shown.
market_premium = - 19E-12 * Intercept
这很奇怪。我检查了数据,看起来很好(虽然很多数据包含0 return_sec,这是正常的,因为有时返回不会在几秒钟内改变,但在几分钟内)。
令我感到困惑的是,当market_premium = - 19E-12 * Intercept时,为什么SAS会在market_premium上返回0系数。我的意思是,当它看到market_premium是Intercept的标量时间时,SAS是否将Intercept视为唯一的变量?