I'm working with time-series and want to get rid of the time dependance, i.e. to get clean series (clean demand if one predicting user demand at some marketplace).
Beginning with the classic paradigm $\text{series}(t) = \text{trend}(t) + \text{seasonality}(t) +\text{residual}(t) $, I can find components of $\text{trend}(t)$ and $\text{seasonality}(t)$ using classical approaches (moving average, STL decomposition), or by using big models (Prophet).
Then one can "subtract" this components from original series and get $\text{residual}(t)$ component, assuming we have clean demand (in my parcticular case) series.
Question is: Is it actually valid way to get rid of the time dependance? Since residual part contains error term in it and can have big impact on the following task (e.g. predicting demand) and cause errors.