NO.PZ2020010801000025
问题如下:
A model was estimated using daily data from the S&P 500 from 1977 until 2017 which included five day-of-the-week dummies (n = 10,087). The from this regression was 0.000599. Is there evidence that the mean varies with the day of the week?
解释:
The model estimated is
,
where Di is a dummy that takes the value 1 if the index of the weekday is i (e.g., Monday = 1, Tuesday = 2, c). The restriction is that
so there this is no day-of-the-week effect. This model can be equivalently written as
,
therefore, here the null is
.
In the two models, , and . The second form of the model is a more standard null for an F-stat.
The F-stat of the regression is
The distribution is an and the critical value using a 5% size is 2.37. The test statistic is less than the critical value, therefore, the null that all effects are 0 is not rejected.
题干中直接说了5dummies为什么列回归式的时候要简化成4个呀。虽然可以理解一周5个工作日,所以只要4个dummy,但是题干中的说法有点迷惑,还以为什么特殊情况考虑一天交易6天。请问考试中遇到类似问题是都要基于常识判断而不是根据题目直接表达的含义吗?谢谢