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Jimmyz · 2024年08月11日

DW检验值与critical value的关系

  1. CFA II
  2. Quantitative

* 问题详情，请 查看题干

NO.PZ202304050200003402

问题如下：

Luke examines West Texas Intermediate (WTI) monthly crude oil price data, expressed in US dollars per barrel, for the 181-month period from August 2000 through August 2015. The end-of-month WTI oil price was $51.16 in July 2015 and $42.86 in August 2015 (Month 181).

He then runs the following regressions using the WTI time-series data.

Linear trend model: Oil pricet = b0 + b1t + et

Log-linear trend model: ln Oil pricet = b0 + b1t + et


In Exhibit 1, at the 5% significance level, the lower critical value for the Durbin–Watson test statistic is 1.75 for both the linear and log-linear regressions. Based on the regression output in Exhibit 1, there is evidence of positive serial correlation in the errors in:

选项：

A.

the linear trend model but not the log-linear trend model.

B.

both the linear trend model and the log-linear trend model.

C.

neither the linear trend model nor the log-linear trend model.

解释：

The Durbin–Watson statistic for the linear trend model is 0.10and, for the log-linear trend model, 0.08. Both of these values are below the critical value of 1.75. Therefore, we can reject the hypothesis of no positive serial correlation in the regression errors in both the linear trend model and the log-linear trend model.

老师可否总结一下，是否只有DW检验值小于critical value，就拒绝原假设。除此之外，t检验，F检验等其他检验值需要大于对应的critical value，就拒绝原假设？

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1 个答案

袁园_品职助教 · 2024年08月12日

嗨，努力学习的PZer你好：


一、DW检验原来二级教材中是给过明确的判断方法的，但是现在删了，因为现在多元回归中DW检验已经被BG检验替代了，只有后面的时间序列分析的课后题里面提到。

所以DW检验现在不是特别的重要。它具体的做法是：

第一步：提出原假设,无序列相关。

第二步：计算DW统计量，公式为： DW=2*（1-r）

式中，r——残差项的自相关系数 。根据这个公式我们可以看出

  1. 若r趋近于0，则表示无序列相关，此时DW趋近于2，说明不存在序列相关现象。
  2. 若r趋近于-1，则表示负序列相关，此时DW趋近于4，说明残差之间存在非常显著的负相关关系。
  3. 若r趋近于+1，则表示正序列相关，此时DW趋近于0，说明残差之间存在非常显著的正相关关系。

第三步：判断。通过查找DW表得到dL和dU（考试中dL和dU通常会直接给出）

二、t检验需要看是单尾还是双尾。

如果是双尾的检验，原假设比如是bi=0。那么拒绝域都是和备择假设一致，所以在两边。

如果是单尾检验，原假设是bi<=0.那么拒绝域就是和备择假设一致，所以在右边

三、F检验是你说的，需要大于对应的critical value，就拒绝原假设

因为F检验是一个单尾检验。我们依据给定的置信水平、分子自由度、分母自由度查询F分布表得到临界值。F检验的决定法则如下：当 检测值> 较大的临界值时，我们就拒绝原假设 。这就代表回归模型中至少存在一个自变量，它的系数显著性不等于零，即回归模型中至少有一个自变量对解释因变量是有效的。

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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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