CROSS: A Reproducible Macroeconomic Forecasting Method Based on Rule-Based Hybrid Neural Architecture

This article introduces the CROSS hybrid neural network architecture, a new macroeconomic forecasting method that combines economic structural models with residual learning. Through a rule-based routing mechanism, it addresses the problems of traditional econometric models' insufficient ability to handle nonlinearity, overfitting and irreproducibility of pure deep learning models, and effectively prevents data leakage in time series forecasting, improving the reliability and interpretability of forecasting results.

Macroeconomic forecasting is a core challenge at the intersection of economics and data science. Traditional econometric models (such as ARIMA, VAR) have strong interpretability but struggle to handle nonlinear relationships and complex economic dynamics; pure data-driven deep learning models have strong forecasting capabilities but are prone to overfitting noise and their results are difficult to reproduce. In addition, the widespread data leakage problem in time series forecasting (accessing future information during training) will seriously overestimate the real performance of the model.

The core idea of the CROSS architecture is to combine economic prior knowledge with data learning capabilities, and automatically select forecasting strategies through a rule-based routing mechanism. Its dual-branch structure includes:

1. Structure branch: Encodes the structural relationships of economic theories to ensure forecasts align with basic logic;
2. Simple branch: Learns residuals (short-term shocks, seasonal fluctuations, etc.) that cannot be explained by structural models. The routing decision module dynamically assigns branch weights based on input features and historical performance, and the decision process is interpretable.

CROSS adopts multiple measures to ensure the authenticity and reproducibility of results: fixing random seed 42 to eliminate fluctuations; strictly splitting training/test sets in chronological order; using only training set data for normalization statistics; constructing lag features before time splitting; routing decisions based only on historical evidence before forecasting; calculating target year errors after forecasting. These measures build a leakage-proof experimental pipeline, close to real forecasting scenarios.

The experiment focuses on Iraq's macroeconomic indicators, using open annual data from the World Bank. Results show that CROSS's forecasting accuracy is significantly better than pure structural models and pure data-driven models, and the results are more consistent (small fluctuations across different seeds and subsets). Routing diagnosis found that when the economy is affected by external shocks (oil price fluctuations, conflicts), the weight of the residual branch increases; during stable periods, the structure branch dominates, verifying the rationality of combining the advantages of different methods.

For policymakers: Provides a reliable tool, and the interpretable routing mechanism allows decision-makers to understand the forecasting logic; For researchers: Demonstrates the idea of combining domain knowledge with machine learning, avoiding absurd conclusions from black boxes; For developers: The data leakage prevention practice provides a checklist, offering a template for rigorous evaluation processes.

Limitations: The design of the structure branch relies on strong domain knowledge, making it difficult to directly apply to emerging economic fields; routing rules depend on expert experience. Future directions: Explore data-driven automatic learning of routing strategies; verify performance on higher-frequency (monthly, quarterly) data; expand to multi-country, multi-indicator joint forecasting.

CROSS represents an important progress in the field of macroeconomic forecasting, finding a middle ground between traditional models and deep learning, combining their advantages to improve forecasting accuracy, interpretability and reproducibility. Its code and experimental data have been open-sourced on GitHub (link: https://github.com/asadollahi2/CROSS_Hybrid_Forecasting), providing a foundation for community improvement and application.