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I am running a linear regression model, and one of my features shows autocorrelation. I’m trying to understand how this affects my model and what the best way to address it might be.

From what I understand, the main issue with an autocorrelated feature is that the standard error (SE) of the coefficient for that feature could be inflated. This happens because the sample variance is biased when there is autocorrelation.

My questions are:

1 - Is an inflated SE for the affected feature's coefficient the only issue? Could autocorrelation also create autocorrelation in the residuals for example?

2 - One way to deal with autocorrelation is to difference the time series. However, if the time series shows serial autocorrelation at different lags, how should I approach this?

3-Do regularization techniques like Ridge or Lasso help resolve issues with autocorrelation?

I’m looking for some intuition or suggestions on how to handle this problem effectively. Thanks!

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  • $\begingroup$ I'm not sure I understand. Are you referring to the autocorrelation of feature values between different samples? $\endgroup$
    – gunes
    Commented Oct 17 at 6:26
  • $\begingroup$ Please describe your data and model in more detail $\endgroup$
    – mkt
    Commented Oct 17 at 10:45
  • $\begingroup$ @gunes exactly. For simplicity I am assuming only one feature is autocorrelated $\endgroup$
    – why_not_me
    Commented Oct 17 at 11:46
  • $\begingroup$ @mkt it's really just a general question to understand how a feature that is autocorrelated can affect a model. As a feature you can take financial price data, energy consumption... $\endgroup$
    – why_not_me
    Commented Oct 17 at 11:47

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