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May I use the Newey-West procedure when I have only autocorrelation?
Or can I only use the Newey-West when I have autocorrelation and heteroscedasticity?

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    $\begingroup$ If you have a regression model with autocorrelated (but not heteroskedastic) residuals, you could run regression with ARMA errors. This would give you more power (narrower confidence intervals) and help in forecasting if needed. Therefore, it could be preferred over using robust standard errors without explicitly modelling the autocorrelation. Search "regression with ARMA errors" here on Cross Validated; there are quite many recent posts on the subject. $\endgroup$ – Richard Hardy Aug 3 '16 at 17:50
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The N-W error structure is assumed to be heteroskedastic and possibly autocorrelated up to some lag.

If you errors are assumed to follow a first-order autoregressive process, you can use Prais-Winsten or Cochrane-Orcutt regression.

If it is longer, ARMA might work.

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    $\begingroup$ I suppose N-W is robust regardless of presence of heteroskedasticity. But would using it be efficient when there is no heteroskedasticity? Could one gain power by using another form of robust errors? I already know one could gain power by using regression with ARMA errors, which is probably the best option here; but I am still curious about alternative versions of robust standard errors. $\endgroup$ – Richard Hardy Aug 3 '16 at 17:55
  • $\begingroup$ @RichardHardy I think N-W would not be as efficient if there's truly no heteroskedasticity. $\endgroup$ – Dimitriy V. Masterov Aug 3 '16 at 20:19
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    $\begingroup$ That's what I think, too. Pardon my nitpicking, but I thought maybe you knew more on the subject and could make your answer more elaborate so that it could serve as a nice reference for similar future questions. $\endgroup$ – Richard Hardy Aug 4 '16 at 6:22
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    $\begingroup$ @RichardHardy I was agreeing with you, but did not make that at all clear. If you had some knowledge of the AR structure, feasible GLS would be the most efficient alternative. $\endgroup$ – Dimitriy V. Masterov Aug 4 '16 at 17:42
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The short answers are YES and YES.

The Newey-West estimator is one of the so called heteroscedasticity and autocorrelation consistent (HAC) estimators of the covariance matrix, it's not the only one out there. It works for any combination of heteroscedasticity and autocorrelation present.

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