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I have time series GDP growth rate data that I use as my Y and other X variables that I put into neural networks to make predictions. The two questions that I have are:

  1. When I decompose my GDP_growth variable I get a detrended variable that I model and make predictions of. If I have train and test data until 2023 and want to make predictions for 2024 them they will likely be way different than the real values as when I removed the trend term I got smaller numbers for the new y. So how to deal with this? When I get predictions of 0.0034 because the data it is fed (after it being decomposed) is between -0.05 and 0.05 interpretability is impossible as the real values are generally bigger than 0.05 and smaller than -0.05. This is not the networks fault as this is all the data that it sees still the interpretability is awful.

  2. When I scale my X's and put new data in (for example the year is 2025 and want to use the same model trained up to 2023 to make predictions) should I train a scaler upto 2023 and apply it to the 2025 data? If so, any unseen data for 2025 will be above the max or below the min of the min-max scaler.

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This is a problem with forward forecasting and min-max scaling. Without digging into your dataset and model architecture, experiment with Robust, Standard, and logarithmic scaling and compare the results of your forward-forecasted data. From personal experience, I have seen significant improvements in performance by using different scalers, even different scalers, for various features. The dataset, as does what you are looking to solve for, also matters.

If you continue with the min-max scaler in how you approach the problem, you will need to find a way to "retrain" your model as the market data changes and deviates. The time interval for the retraining takes much analysis to figure out and is no small feat as it is influenced by far more than just time. However, if you want something that works well and is manageable, change the scaler and optimize your dataset.

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