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大老王 · 2023年04月12日

T 的数额

  1. CFA II
  2. Quantitative

* 问题详情，请 查看题干

NO.PZ201709270100000406

问题如下：

6. Based on the data for the AR(1) model in Exhibits 1 and 2, Martinez can conclude that the:

选项：

A.

residuals are not serially correlated.

B.

autocorrelations do not differ significantly from zero.

C.

standard error for each of the autocorrelations is 0.0745.

解释：

C is correct. The standard error of the autocorrelations is calculated as 1T\frac{1}{\sqrt{T}}, where T represents the number of observations used in the regression. Therefore, the standard error for each of the autocorrelations is 1180\frac{1}{\sqrt{180}} = 0.0745. Martinez can conclude that the residuals are serially correlated and are significantly different from zero because two of the four autocorrelations in Exhibit 2 have a t-statistic in absolute value that is greater than the critical value of 1.97.

Choices A and B are incorrect because two of the four autocorrelations have a t-statistic in absolute value that is greater than the critical value of the t-statistic of 1.97.

请问本题中求 standard error中为什么T 或者说N 是180而不是181呢，我是拿1/ √181 这么算的

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1 个答案

星星_品职助教 · 2023年04月12日

同学你好，

1）理解角度：可以从AR模型的形式来理解这个数字。AR是自己和自己做回归，即Xt=b0+b1Xt-1。可以看出，如果一共有t个值，那么有一个值就要分给等式左侧的因变量（即Xt会占用一个值），用于等式右侧回归的自变量的值就只有t-1个；

2）解题角度：实际做题中并不用自己去数数字。常规情况下，题干中会给出一个表格，从表格中直接找到“observations”这一行的数字就可以用。因为无论用字母T还是N，公式的本质都是1/ √observations。

例如下面这种情况，直接代入1/ √65即可。

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