Forecasting US M2 Money Supply: Linear vs. Non-Linear Models

This project explores the predictability of the monthly growth rate of the US M2 Money Supply, comparing the efficacy of traditional linear econometric models against non-linear Machine Learning algorithms.

The analysis covers an extended time horizon (1959–2025), placing particular emphasis on model robustness during the liquidity shock caused by the COVID-19 pandemic in 2020.

🎯 Project Goal

To determine whether the complexity of non-linear models (ML) offers a predictive advantage over parsimonious linear models in a macroeconomic context characterized by structural breaks and high volatility.

📊 Data

Data is sourced from the FRED (Federal Reserve Bank of St. Louis) database:

• Target: M2SL (M2 Money Supply, Seasonally Adjusted).
• Exogenous Regressor (for VAR): FEDFUNDS (Effective Federal Funds Rate).
• Range: January 1959 – October 2025.
• Transformations: Data has been transformed via Log-Difference to ensure stationarity (Monthly Growth Rate).

🛠️ Methodology and Models

The study compares three modeling approaches using 1-step ahead rolling forecasts:

1. ARIMA (Univariate - Benchmark):
   • Parameter selection $(p,d,q)$ via Grid Search minimizing AIC.
   • Optimal model identified: ARIMA(4,0,3).
2. Vector Autoregression (VAR - Multivariate):
   • Includes Interest Rates (FEDFUNDS) to test the impact of the cost of money on money supply.
   • Lag selection via AIC ($k=13$).
3. Random Forest (Machine Learning - Non-Linear):
   • Supervised learning approach with 12 time-lag features.
   • Ensemble of 100 decision trees.

📂 Repository Structure

The code is organized into sequential Jupyter Notebooks to ensure reproducibility:

• notebooks/
  • 01_data_prep.ipynb: Data loading, stationarity tests (ADF), transformations, and Train/Test split (80/20).
  • 02_modeling.ipynb: ARIMA model estimation and Grid Search.
  • 03_ml_model.ipynb: Feature engineering and Random Forest training.
  • 04_var_model.ipynb: Multivariate dataset creation and VAR model estimation.
  • 05_evaluation.ipynb: Final comparison, metrics calculation (RMSFE, MAFE), and plot generation.
• data/: Raw CSV files (M2SL.csv, FEDFUNDS.csv).
• results/: Comparison tables and exported plots.

📈 Key Results

The empirical analysis on the Test Set (2012-2025) yielded the following results:

Model	Type	RMSFE	MAFE	Bias
ARIMA (4,0,3)	Linear / Univariate	0.5455	0.2703	-0.0168
VAR (13)	Linear / Multivariate	0.5462	0.2677	-0.0143
Random Forest	Non-Linear / ML	0.6503	0.3038	0.0034

Main Conclusions:

• Linear models (ARIMA and VAR) dominate in terms of accuracy, successfully adapting to the 2020 shock due to the strong autoregressive inertia of the series.
• Random Forest, despite having the lowest Bias (unbiased on average), fails to capture volatility peaks due to the inability of decision trees to extrapolate values outside the training range (bounding box problem).
• Adding interest rates in the VAR model slightly improves the Mean Absolute Forecast Error (MAFE) but does not enhance outlier handling (RMSFE).

💻 Installation and Usage

1. Clone the repository:

   git clone [https://github.com/your-username/m2-forecasting.git](https://github.com/your-username/m2-forecasting.git)

2. Install required dependencies:

   pip install pandas numpy matplotlib scikit-learn statsmodels

3. Run the notebooks in numerical order from 01 to 05.

📜 License

This project is distributed under the MIT License.