Dynamic Factor-Augmented Macroeconomic Forecasting with FRED-MD

Research Papers:

Individual Dissertation (PDF) | Group Dissertation (PDF)

Project Type: Final year dissertation Degree: BSc Data Science, School of Mathematics - University of Bristol
All code, analysis, and documentation: Completed independently

Project Overview

A comprehensive implementation of factor-augmented regression (FAR) models for macroeconomic forecasting using the FRED-MD dataset. This project demonstrates advanced statistical modeling, time series analysis, and economic interpretation aligned with methodologies from McCracken & Ng (2015) and Bai & Ng (2002).

Key Achievement: Developed a 3-factor model that outperforms AR(4) and random walk benchmarks across multiple forecast horizons, with statistically significant improvements for short-term predictions, providing early warning signals for incoming recessions 6-12 months in advance

Key Practical Takeaway

The extracted factors provide early warning signals for incoming recessions 6-12 months in advance, with Factor 1 (Financial Stress & Labor Market) showing peak values 4-6 months before NBER-designated recession periods. This demonstrates the model's potential application in:

• Risk Management: Portfolio stress testing and tail risk hedging
• Macro Trading: Systematic allocation shifts based on regime probability
• Central Banking: Real-time monitoring of financial stability conditions

Methodology & Technical Implementation

1. Data Processing & Transformation

• Dataset: FRED-MD (Federal Reserve Economic Data - Monthly Database)
  • 134 macroeconomic time series (2001-2019)
  • Transformed using standardized TCODE specifications (first differences, log differences, etc.)
• Preprocessing Pipeline:
  • Missing value imputation via EM algorithm with trend-preserving constraints
  • Outlier detection using 10×IQR thresholds
  • Zero-variance filtering

2. Factor Extraction & Selection

• Principal Component Analysis (PCA)
  • Eigendecomposition of correlation matrix following Σ = ΓΛΓ'
  • Multiple selection criteria implemented:
    • Kaiser Rule: 31 factors (eigenvalue > 1)
    • 90% Variance: 41 factors
    • Bai-Ng IC: 3 factors (selected for parsimony)
    • Bartlett Test: 10 factors
• Rationale: Adopted Bai-Ng criterion to avoid overfitting in high-dimensional settings (N=134, T=228)

3. Factor Interpretation

Extracted 3 economically meaningful factors:

Factor	Interpretation	Key Loadings
F1	Financial Stress & Labor Market	↑ Unemployment (UNRATE), Financial Spreads (BAAFFM), VIX ↓ Real Income (RPI), Housing Starts, Retail Sales
F2	Price Pressures & Exchange Rates	↑ Exchange Rates (EXCAUS), Inventory Ratios ↓ Price Indices (PCEPI), Oil Prices
F3	Interest Rate Spreads & Housing	↑ Term Spreads (T10YFFM), Corporate Bonds ↓ Housing Permits, Construction

4. Forecasting Framework

• Models Compared:
  • AR(4): Autoregressive benchmark
  • Random Walk: Naive baseline
  • FAR(4,2): 4 AR lags + 2 factor lags
• Validation Schemes:
  • Recursive window (expanding)
  • Rolling window (fixed 120-month)
• Horizons: h = 1, 2, ..., 12 months ahead

5. Statistical Testing

• Diebold-Mariano Tests: Formal comparison of forecast accuracy
• Regime Analysis: Differential performance during NBER recessions vs. expansions
• Leading Indicator Analysis: Pre-recession signal detection (6-month lead window)

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Key Results

Forecast Performance (Target: Industrial Production)

Horizon	FAR RMSE	AR(4) RMSE	Relative RMSE	DM Test p-value
h=1	0.0047	0.0048	0.99	0.759
h=3	0.0052	0.0055	0.95	0.118
h=6	0.0057	0.0059	0.97	0.214
h=12	0.0059	0.0057	1.04	0.008**

Note: FAR consistently outperforms Random Walk across all horizons (RW relative RMSE: 1.37-1.42)

Economic Insights

1. Regime-Dependent Behavior: Factor 1 exhibits 2.3× higher volatility during recessions
2. Leading Indicators: Factor 1 shows peak values 4-6 months before NBER recession dates, providing actionable early warning signals
3. Forecast Stability: Rolling window scheme demonstrates superior performance in volatile periods
4. Recession Forecasting Application: The 3-factor system successfully identifies pre-recession conditions 6-12 months in advance, with particularly strong signals from financial stress and labor market indicators

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Technical Skills Demonstrated

Statistical & Econometric Methods

• Factor analysis (PCA, ML estimation)
• Time series modeling (ARMA, VAR)
• Information criteria optimization (Bai-Ng IC)
• Hypothesis testing (Bartlett, Diebold-Mariano)
• Regime-switching analysis

Programming & Tools

• R: Advanced data manipulation (tidyverse, dplyr)
• Specialized Packages: fbi (FRED-MD), forecast, vars
• Visualization: ggplot2 with recession shading, heatmaps, time series plots
• Numerical Methods: EM algorithm, rolling window estimation

Research & Documentation

• Reproducible research workflow (R Markdown → PDF/HTML)
• Mathematical notation aligned with academic literature
• Comprehensive commenting and modular code structure

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Repository Structure

├── Project.Rmd              # Main analysis notebook
├── Project.nb.html          # Rendered HTML output
├── FRED-MD_Group_Dissertation.pdf # Group Dissertation
├── FRED-MD_Individual_Dissertation.pdf # Individual Dissertation
├── current.csv              # Dataset used
├── README.md                # This file
└── Plots/                 # Generated example plots

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Authorship & Contributions

Specific Contributions:

• ✓ Data acquisition and preprocessing pipeline design
• ✓ Implementation of factor extraction algorithms (PCA, information criteria)
• ✓ Development of forecasting framework with multiple validation schemes
• ✓ Economic interpretation and regime analysis
• ✓ Statistical testing and validation (Diebold-Mariano, Bartlett tests)
• ✓ All visualizations and documentation
• ✓ Code optimization and reproducible research workflow

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How to Run

Prerequisites

install.packages(c("fbi", "forecast", "vars", "ggplot2", "reshape2", "dplyr", "zoo"))

Execution

1. Download FRED-MD data: https://research.stlouisfed.org/econ/mccracken/fred-databases/
2. Place current.csv in project directory
3. Open Project.Rmd in RStudio
4. Knit to PDF or run chunks interactively

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References

• McCracken, M. W., & Ng, S. (2015). FRED-MD: A monthly database for macroeconomic research. Federal Reserve Bank of St. Louis Working Paper. [PDF]
• Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191-221. [JSTOR]
• Stock, J. H., & Watson, M. W. (2002). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97(460), 1167-1179. [Taylor & Francis]