Autocovariance in residuals of time series regression indicates that OLS should never be applied to estimate coefficients

Question

BlackTom AI · Accepted Answer

We start by restating the prompt to focus on the core idea: whether autocovariance in the residuals from a time series regression implies that OLS should never be used to estimate coefficients.
Option 1: True. The claim here is that autocovariance in residuals means OLS should never be applied. This is inaccurate. While autocorrelation of residuals violates one of the Gauss-Markov assumptions that give OLS its optimality properties under homoskedastic, uncorrelated errors, it does not mean OLS cannot be used at all. The estimators of the coefficients remain unbiased and consistent under standard OLS even with autocorrelated errors, provided the regressors are exogenous. The problem is that the usual standard errors and test statistics become unreliable, leading to invalid inference. So this statement is incorrect because it overstates the consequence of autocovariances.
Option 2: False. This option correctly captures the nuanced reality. Autocovariance in the residuals indicates serial correlation, which means the OLS estimators are not as efficient as they could be (they lose the Gauss-Markov efficiency), and the standard errors are biased, affecting inference. However, OLS can still be applied to estimate the coefficients; to obtain valid inference, one would typically adjust standard errors (e.g., using Newey-West HAC standard errors) or switch to a method that models the correlation structure directly (e.g., generalized least squares, GLS). This option aligns with standard econometric practice and correctly distinguishes estimation from inference issues.
A quick comparison helps reinforce the distinction: if residuals are autocorrelated, estimation may still proceed with OLS, but the usual t-tests and F-tests are no longer trustworthy unless corrected. Conversely, claiming OLS should never be used ignores the practical use of OLS as a baseline estimator and the remedies available for inference.
In summary, the erroneous option is the first one, which claims impossibility of using OLS, whereas the second option correctly notes the caveats and remedies related to autocorrelation in residuals.

AS.440.617.80.SP25 Quiz 4. Time Series regression

Autocovariance in residuals of time series regression indicates that OLS should never be applied to estimate coefficients

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