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I have two models to predict future stock market behavior based on historical data:

  1. ARIMA time series model
  2. lstm model (including data from various other sources)

ARIMA tries to model the daily diffs in stock market ('removed trend of time series'), while LSTM predicts the absolute value. To combine both predictions I use an xgboost model.

Is it necessary to normalize the input features of xgb to either diffs or absolute value? Is this irrelevant since xgb runs a regression model at every leaf - or is scaling necessary?

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Any Gradient Boosting Machine (GBM) method that uses trees as its base-learners is not strongly affected by the scale of the input data. In that sense, using differences or absolute values is somewhat unimportant. If the GBM algorithm uses linear models as its base-learner (i.e. in XGBoost we use gblinear as a base-learner) then the scale of the input features is relevant. This said, it would be potentially beneficial for debugging and/or comparing feature importances to use data that are on the same scale, the comparison would be more straightforward.

On a somewhat parallel note, I would suggest being very careful how time-series cross-validation is performed especially when ensembling models. It is important not to have future information "leak" in our training procedure.

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