Can autocorrelation confound causal inference?

Question

I'm working with a weekly aggregated time series that has autocorrelation and I'm trying to find out why the trend has been decreasing by regressing other features onto - I noticed that when I use an ARIMA to account for autocorrelation, it masks some features that wouldn't have been masked from OLS.

In the case of this time series, there's certainly yearly seasonality, but when it comes to short term lags there's really no reason to believe that they have a causal influence on eachother, its more likely just caused by the fact that they occur within the same seasonality.

Is it better to use something like OLS in this case and ignore the fact that there's autocorrelation in the errors? Or is there justification for still accounting for the autocorrelation? If so, what is it?

Answer 1

You want your model to be not only theoretically adequate but also statistically adequate. For a methodological discussion on that, see the Probabilistic Reduction methodology by Aris Spanos; I have summarized it in my earlier post "Effects of model selection and misspecification testing on inference: Probabilistic Reduction approach (Aris Spanos)".

If you have autocorrelated errors while your model assumes uncorrelated ones, you violate statistical adequacy. You can do that and may still get consistent estimators (though not always! see Christoph Hanck's answer) and in such cases even do valid inference if you adjust your standard errors for autocorrelation, but you lose efficiency (i.e. your point estimates could be improved upon); a cleaner approach is to model the structure in the errors explicitly. Francis X. Diebold also advocates that; see these threads (e.g. start by this) for references and examples of applying his argument.