METHODOLOGY

AUTO-ARIMAX
Model

Our forecasting engine combines autoregressive integrated moving average models with exogenous variables, automatically optimized for each economic indicator.

Model Architecture
ARIMAX (AutoRegressive Integrated Moving Average with eXogenous variables)

The AUTO-ARIMAX model extends traditional ARIMA by incorporating external economic variables that influence the target indicator. Our system automatically determines optimal parameters through rigorous statistical testing.

  • AR (p): Autoregressive order - captures dependence on past values
  • I (d): Integration order - handles non-stationarity through differencing
  • MA (q): Moving average order - models forecast errors
  • X: Exogenous variables - incorporates related economic indicators
Evaluation Metrics
How we measure model performance

Mean Absolute Error (MAE)

Average magnitude of forecast errors. Lower values indicate better accuracy. Provides intuitive interpretation in the same units as the target variable.

Root Mean Squared Error (RMSE)

Square root of average squared errors. Penalizes larger errors more heavily than MAE, making it sensitive to outliers and extreme forecast deviations.

Mean Absolute Percentage Error (MAPE)

Average percentage deviation from actual values. Scale-independent metric allowing comparison across different indicators with varying magnitudes.

Direction Accuracy

Percentage of forecasts correctly predicting the direction of change (up/down/flat). Critical for trading and policy decisions where trend direction matters more than exact values.

Data Sources
FRED (Federal Reserve Economic Data)

All economic data is sourced from the Federal Reserve Bank of St. Louis's FRED database, the most comprehensive and authoritative source of U.S. economic statistics.

FRED provides high-frequency updates, rigorous data quality standards, and extensive historical coverage essential for robust time series modeling. Our system automatically retrieves the latest data releases to ensure forecasts reflect current economic conditions.

Academic Foundation
Research-backed methodology

Our approach builds on decades of econometric research in time series forecasting. Key methodological foundations include:

  • Box-Jenkins methodology for ARIMA model identification
  • Akaike Information Criterion (AIC) for model selection
  • Augmented Dickey-Fuller tests for stationarity assessment
  • Rolling window validation for out-of-sample performance evaluation

Models are retrained monthly with expanding data windows to incorporate new information while maintaining statistical rigor.