CFA Level II ExamQuantitative MethodsHard
An investment bank is using a multiple regression model to explain the returns of a specific hedge fund based on several market factors. The model's regression output shows a Durbin-Watson statistic of 0.85 for a sample size of 100 observations and 3 independent variables. The critical values for dL and dU at a 5% significance level are 1.63 and 1.74, respectively. Based on these statistics, what conclusion can be drawn regarding the model's residuals?
- AThe test is inconclusive regarding autocorrelation.
- BThere is no evidence of autocorrelation.
- CThere is negative first-order autocorrelation.
- DThere is positive first-order autocorrelation.
Show answer & explanationAnswer & explanation
Correct answer: D. There is positive first-order autocorrelation.
The Durbin-Watson statistic is used to test for first-order autocorrelation. With d=0.85, dL=1.63, and dU=1.74: since d < dL (0.85 < 1.63), we reject the null hypothesis of no positive autocorrelation. This indicates strong evidence of positive first-order autocorrelation.
Why the other options are wrong
- A. The test is conclusive. When d < dL, there is clear evidence of positive autocorrelation. Inconclusive results occur when dL < d < dU.
- B. If d > dU, there would be no evidence of positive autocorrelation. Here, d < dL, indicating positive autocorrelation.
- C. Negative first-order autocorrelation would be indicated if d > 4 - dL. Here, 4 - dL = 4 - 1.63 = 2.37. Since 0.85 is not greater than 2.37, there is no evidence of negative autocorrelation.
Durbin-Watson Test
The Durbin-Watson test is a statistical test used to detect the presence of autocorrelation (specifically, first-order serial correlation) in the residuals from a regression analysis. Its value ranges from 0 to 4.
- Hypothesis: H0: no positive autocorrelation; Ha: positive autocorrelation.
- Test statistic 'd' around 2 indicates no autocorrelation.
- d < dL: positive autocorrelation.
- 4 - d < dL: negative autocorrelation.
- dL < d < dU or 4 - dU < d < 4 - dL: inconclusive.
Memory trick: DW: Low means positive, High means negative, Middle is inconclusive.