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三言午寺 · 2024年10月30日

不是多元回归是DW检验，线性回归不能用DW检验么？

  1. CFA II
  2. Quantitative

* 问题详情，请 查看题干

NO.PZ202304050200003402

问题如下：

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.

不是多元回归是DW检验，线性回归不能用DW检验么？应该是直接看rho呀

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发亮_品职助教 · 2024年10月31日

不是多元回归是DW检验，线性回归不能用DW检验么？

不是哦，DW检验是专门用来检验autocorrelation/Serial correlation的

DW的问题是，只能用于一阶自相关（first-order serial correlation）or（first order autocorrelation）

一阶自相关描述的是当前数据点和紧邻前一个数据点之间的线性关系，例如，第t个error数据和上一个紧邻的error数据t-1，这两个数据的自相关性。

如果想要研究第t个error数据，和往前退5个error数据、第（t-5）个数据的自相关性，那就不能用DW检验了，这中间跨越了好几个数据。这时候只能用Breusch–Godfrey (BG) test，即BG检验。

这是DW检验的局限性，DW只能检验相邻的2个数据的自相关性。

 

DW检验可以检验线性回归，无论是多元线性还是一元线性回归，都可以使用。

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