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银色羽毛 · 2025年01月18日

standard error的计算不明白

  1. CFA II
  2. Quantitative

NO.PZ2023040502000013

问题如下：

The following exhibit is the results of a regressionof the monthly return for an electric utility equity index for the previous 203months (the dependent variable) against the monthly returns for the S&P 500Index and the difference between the monthly returns on long-term U.S.government bonds and one-month U.S. Treasury bills (SPREAD) (the twoindependent variables).


Hamilton wants to test the null hypothesis that thecoefficient on SPREAD is equal to 1 against the alternative hypothesis that itis not equal to 1. Based on the results in Exhibit 1, the value of the teststatistic relating to Hamilton’s null hypothesis about the value of the coefficienton SPREAD is closest to:

选项：

A.

4.28

B.

0.24

C.

0.11

解释：

The null hypothesis is H0: bspread= 1.

The calculated value of the t-statistic is t = (1.0264 – 1.0)/standarderror.

The standard error is 1.0264/4.28 = 0.24.

The calculated value for t= (1.0264 – 1.0)/0.24 = 0.11.

standard error的计算不明白，为什么是1.00264/4.28？为什么不是standard error=（1.00264-1）/t-statistic？我看了其他的回答，说standard error=1.00264/4.28默认b1=0，可是H0是假设b1=1的，为什么又会b1=0？ 另外我读题有点没读明白，题目里的表格已经给了一个t-statistic，又叫我们算t-statisic是什么意思？

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1 个答案

品职助教_七七 · 2025年01月19日

嗨，努力学习的PZer你好：


表格中的t-statistics都是基于原假设为系数等于0时计算出来的t统计量。要计算的t-statistic是基于原假设为系数=1时的t统计量。这两个t统计量不相等。后者需要手动计算。

使用b1=0的原假设，是为了求出standard error的。已知bspread=0时的t-statistic=4.28，代入t统计量的公式：

t-statistic=（当前系数估计值-原假设假设的值）/standard error，得到：

4.28=（1.0264-0）/standard error。由此求出standard error=1.0264/4.28 = 0.24，无论原假设为系数是多少，对应的standard error都不变,。

只有在已知standard error后，才能够求bspread=1时的t-statistic。同样代入上面的公式，得到：

t-statistic=（1.0264-1）/0.24，从而得到答案0.11。



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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2023040502000013问题如下 The following exhibit is the results of a regressionof the monthly return for electric utility equity inx for the previous 203months (the pennt variable) against the monthly returns for the S P 500Inx anthe fferenbetween the monthly returns on long-term U.S.government bon anone-month U.S. Treasury bills (SPREA (the twoinpennt variables).Hamilton wants to test the null hypothesis ththecoefficient on SPREis equto 1 against the alternative hypothesis thitis not equto 1. Baseon the results in Exhibit 1, the value of the teststatistic relating to Hamilton’s null hypothesis about the value of the coefficienton SPREis closest to: A.4.28B.0.24C.0.11 The null hypothesis is H0: bsprea 1. The calculatevalue of the t-statistic is t = (1.0264 – 1.0)/stanrrror. The stanrerror is 1.0264/4.28 = 0.24. The calculatevalue for t= (1.0264 – 1.0)/0.24 = 0.11. 这里的st error为什么不是开根n分之一

2024-04-13 17:15 2 · 回答

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2023-08-02 17:14 2 · 回答