Are facebook prophet prediction intervals wider when there is autocorrelation in the residuals or no?

I am trying to fit a facebook prophet model to time series data that has multiple seasonalities: daily, weekly, and yearly.

When I fit the model, there is substantial remaining autocorrelation in the residuals, as shown on the ACF plot of the residuals. This means there is information left in the residuals which should be used in computing forecasts.

Are the prediction intervals that I get going to be wider to account for this uncertainty of the information not captured? Or are the prediction intervals going to be narrower than they should be? If they are narrower than they should be then I guess they cannot be used for anomaly detection?

I am confused because in the book "Forecasting Principles and Practice" 3rd edition, in section 12.3 about the Prophet model is says: "There is also substantial remaining autocorrelation in the residuals, As a result, the prediction intervals are probably too narrow." However, in section 7.3 it says: "The forecasts from a model with autocorrelated errors are still unbiased, and so they are not “wrong”, but they will usually have larger prediction intervals than they need to. Therefore we should always look at an ACF plot of the residuals."

Thank you!

Referred here by Forecasting: Principles and Practice, by Rob J Hyndman and George Athanasopoulos

Autocorrelations represent information not captured by the model. So if the model was able to take this information into account, the residuals would be uncorrelated, and the prediction intervals would be narrower.

I have now corrected the statement regarding the prophet model.


Thank you very much for the prompt reply!

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