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I heard a term "ARMA ERROR" in BATS and TBATS. How it helps in time series forecasting.

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First, you could read the paper that introduced the method: https://robjhyndman.com/publications/complex-seasonality/

But that might be hard going if you don't have a statistics background. If you just want to know what an ARMA model is, check out this chapter from my textbook: https://otexts.org/fpp2/arima.html

To see an ARMA error in a model that is easier to understand than a (T)BATS model, look at regression models with ARMA errors, discussed in a later chapter: https://otexts.org/fpp2/dynamic.html

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