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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.

taciturno
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    Whether this is "valid" will depend on what you want to do. Of course you can always apply the STL decomposition and use the residuals, but whether this gives you something helpful is not clear. If your series has autoregression, STL won't remove that, it will just yield autoregressive residuals. What would "getting rid of time dependence" mean for an AR series? Finally, if you want to forecast, the resources here may be helpful. While STL is a well-established tool in forecasting, it's usually not used to "get rid of" something. – Stephan Kolassa Jan 15 '24 at 13:03

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