Question

In estimating a regression based on monthly observations from January 1987 to December 2002 inclusive, you find that the coefficient on the independent variable is positive and significant at the 0.05 level. You are concerned, however, that the t−statistic on the independent variable may be inflated because of serial correlation between the error terms. Therefore, you examine the Durbin-Watson statistic, which is 1.8953 for this regression.

Perform a statistical test to determine if serial correlation is present. Assume that the critical values for (4) 192 observations when there is a single independent variable are approximately dl ≈ 1.74 and du ≈ 1.78.

Answer 1

The hypotheses usually considered in the Durbin-Watson test are

$H_0: \rho = 0$

$H_1: \rho \ne 0$

We reject H₀ when d < dl or d > (4 - dl )

and Retain H₀ when du < d < (4−du)

Durbin-Watson statistic, d = 1.8953

dl ≈ 1.74 and du ≈ 1.78.

4 - dl = 4 - 1.74 = 2.26

4 - du = 4 - 1.78 =  2.22

Thus,

du < d < (4−du) {1.78 < 1.8953 < 2.22}

Thus, we retain H0 and conclude that there is no significant evidence that there is serial correlation between the error terms.