Is using contemporaneous components to forecast an aggregate a valid method or a form of data leakage?

External question — Cross Validated Stack Exchange Author: PSE Original post: https://stats.stackexchange.com/questions/670272 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I am in the middle of a deep methodological debate regarding a time series forecasting problem and would appreciate the community's expert opinion. The Context I am trying to forecast an aggregate time series, which we can simplify as the US CPI ( Aggregate_t ). My dataset is monthly, from Jan 1999 to Aug 2025. I have three types of variables: The target series itself: Aggregate_t . Its two main components (for simplicity): Component_A_t (e.g., Goods) and Component_B_t (e.g., Services). A set of external, exogenous variables, which we can call Exogenous_t . The crucial point is that the aggregate is a deterministic function of its components: Aggregate_t is, by definition, a weighted average of Component_A_t and Component_B_t . The Backtesting Framework My goal is to backtest a model (like LASSO or XGBoost) using an expanding window approach. My full dataset runs until August 2025 . My backtest loop uses expanding windows, with the data_base (the last point of information for a given forecast origin) running from, for example, Jan 2017 up to July 2025 . I stop the data_base loop in July 2025 so that for this final point, the true value for August 2025 is available in my dataset to evaluate the h=1 forecast. The Methodological Debate The core of my debate is how to correctly build the feature set s_t for a given data_base t (e.g., July 2025 ) to predict the target t+1 (e.g., August 2025 ). My Position: My argument is that I should use all information available at time t . Since the values for Component_A_July , Component_B_July , and Exogenous_July are all known, they are all valid features. My proposed feature set s_t would therefore include: Contemporaneous values of the components ( Component_A_t , Component_B_t ). Contemporaneous values of the exogenous variables ( Exogenous_t ). Lags of all variables ( Aggregate_{t-1} , Component_A_{t-1} , Exogenous_{t-1} , etc.). The AI's Position: I've had a long and detailed debate with an AI assistant (Gemini) who strongly argues against this. The AI's position is that including the contemporaneous components ( Component_A_t , Component_B_t ) constitutes a form of identity or proxy leakage . The AI's reasoning is that any flexible model will first learn the near-perfect deterministic relationship Aggregate_t ≈ w1*Component_A_t + w2*Component_B_t . The model then uses this reconstructed Aggregate_t to trivially predict Aggregate_{t+1} due to the series' high autocorrelation. The AI claims this contaminates the experiment, as the model ignores more subtle signals from the lags and exogenous variables, leading to inflated backtest metrics and a non-robust model that has not learned any true economic dynamics. I find it very difficult to accept the AI's position, as I am not leaking any future information. I am simply using all available data from the present ( t ) to predict the future ( t+1 ). The Question For this specific backtesting setup, where the target y_{t+h} is known within the historical dataset for every step of the loop: Is it a methodologically sound practice to include contemporaneous components (Component_A_t, Component_B_t) in the feature set s_t to predict Aggregate_{t+h}? Or does this indeed represent a form of proxy leakage that invalidates the evaluation of the other predictors and leads to overly optimistic results, as the AI suggests? P.S. Empirical Results from an A/B Test To add empirical context, I have run the backtest for both scenarios using real data. Method A (My hypothesis): Including the contemporaneous components. Method B (The AI's "clean" recommendation): Excluding the contemporaneous components. Here are the results for the h=1 forecast RMSE: For LASSO: The results were surprisingly almost identical. Method A (with the shortcut) had an RMSE of ~0.396 , while Method B (clean) had an RMSE of ~0.395 . The interpretation seems to be that LASSO's L1 regularization effectively handled the multicollinearity and "defended" itself from the shortcut by zeroing out redundant features. For XGBoost (untuned): The results were different. Method B (clean) had a relatively high RMSE of ~0.432 . Method A (with the shortcut) improved upon this, with an RMSE of ~0.407 . This empirical result adds to my confusion. The shortcut seems to exist (it helps the XGBoost model), but it's not as catastrophic as the AI initially predicted, and the simpler LASSO model seems robust to it and performs better overall. This reinforces my question about whether including these features is a truly invalid practice or just a risky one with specific trade-offs depending on the model used.

External answer — Cross Validated Stack Exchange Author: Stephan Kolassa Original post: https://stats.stackexchange.com/a/670273 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. You are completely correct, and Gemini is wrong. The model then uses this reconstructed Aggregate_t to trivially predict Aggregate_{t+1} due to the series' high autocorrelation. Well, but that is wonderful! If your goal is to predict Aggregate , based on your two components, and the total has such a high autocorrelation that it is easy to forecast without using the separate components , then why in the world would you not do that? Disregard Gemini and move on. (Alternatively, use a hierarchical reconciliation step: forecast the Aggregate by itself, and also calculate the weighted average between the forecasted components, which will give you a different forecast of the Aggregate. I strongly suspect that the average of these two forecasts will be better than either one.)