FRM Part I · FRM Exam Part I · Regression Diagnostics
An analyst plots residuals of a time-series regression in date order and sees long runs of positive residuals followed by long runs of negative residuals. Which Durbin-Watson statistic is most consistent with this plot?
Long runs of same-signed residuals indicate positive autocorrelation. Because the Durbin-Watson statistic is approximately 2(1−ρ), positive correlation pushes it well below 2, so a value around 0.6 is consistent. Values near 2 imply no autocorrelation and values near 4 imply negative autocorrelation.
- AAbout 2.0
- BAbout 3.8
- CAbout 0.6Correct
- DAbout 0.0 exactly because residuals sum to zero
Explanation
Long runs of same-signed residuals indicate positive serial correlation. The Durbin-Watson statistic is approximately 2(1−ρ), so ρ near 0.7 gives about 0.6. A value near 2 means no correlation and a value near 4 means negative correlation.
Did you get it right without looking?
One question tells you little. A timed set on Regression Diagnostics shows your real accuracy, how long you take and where you lose marks.
More Regression Diagnostics questions
- A regression has residual standard error s = 2.0. One observation has residual e = 7.0 and leverage h = 0.19. Using the internally studentiz…
- In a cross-sectional regression of household food spending on household income, the dispersion of the residuals grows steadily as income ris…
- A risk manager estimates a time-series regression by OLS and finds the residuals are positively autocorrelated, while the regressors are not…
- After fitting a multiple regression, an analyst finds that a plot of residuals against a regressor shows a systematic U-shaped pattern. Whic…
- In a multiple regression of a fund's excess return on several factor returns, an analyst finds that the R-squared is high and the F-test is …
- A risk analyst is concerned about severe multicollinearity between two regressors, X1 and X2, in a model used to forecast portfolio losses. …