When a linear regression model yields correlated errors it is claimed that the standard error of the estimators is under estimated. Can anyone give a proof of this fact? This is stated on page 94 of Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani
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Check this: http://stats.stackexchange.com/questions/114564/why-autocorrelation-affects-ols-coefficient-standard-errors – Dole Apr 10 '16 at 01:13
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A proof is impossible because the statement is false. When the errors are strongly *negatively* correlated, then the standard error of the estimators will be overestimated. Refer back to your source of the claim to check what additional assumptions or qualifications it is making--and please let us know what this source is. – whuber Apr 10 '16 at 15:29