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I run an OLS, after check residuals, they are normally distributed, mean is zero with some randomness. But after the autocorrelation plot shows significant correlations to 15+ lags. What should I do next to avoid this autocorrelation?

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It would be useful to know what you are trying to estimate, is this a time series regression, cross-sectional, etc? If it's time series, you could try a first difference and then proceed with an ARMA model

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