FRM Part I · FRM Exam Part I · Regression Diagnostics
An analyst regresses monthly excess returns of a fund on a market factor using time-series data. A plot of the residuals shows long runs of positive residuals followed by long runs of negative residuals. Which conclusion is most consistent with this pattern?
Long runs of same-signed residuals signal positive serial correlation. OLS coefficient estimates stay unbiased, but the usual standard errors tend to be understated, which makes t-statistics too large and significance tests overly optimistic.
- ANegative serial correlation in the residuals, so OLS slope estimates are biased
- BPositive serial correlation in the residuals, so OLS standard errors are likely understatedCorrect
- CHeteroskedasticity only, so the slope estimates are inconsistent
- DPerfect multicollinearity among the regressors
Explanation
Long runs of same-signed residuals indicate positive first-order serial correlation. With positive autocorrelation, conventional OLS standard errors are typically too small, inflating t-statistics. Slopes remain unbiased (if regressors are exogenous), so the bias claim is wrong.
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