To validate model robustness, we first conducted in-sample testing using our LSTM architecture optimized via Bayesian Optimization (BO). This phase evaluated the model’s ability to fit historical data and learn structural yield dynamics under known macroeconomic conditions.
We trained the LSTM using macroeconomic features that were first standardized, then transformed via Principal Component Analysis (PCA). The resulting time series input was passed into the LSTM for sequence learning, enabling it to capture temporal dependencies across multiple maturities.
Bayesian Optimization was employed to identify the optimal combination of hyperparameters, including:
This allowed us to efficiently search the hyperparameter space while minimizing loss and avoiding overfitting.
Using the best model configuration (time_steps=60, unit='w'):
| MSE | 0.000641 |
| RMSE | 0.0253 |
| MAE | 0.0197 |
| R² | 0.9864 |
✅ R² of 0.986 indicates the model captures nearly all the variance in the training data — a hallmark of strong fit.
⚙️ The optimized parameters (lstm_units=71, dropout≈10.8%, batch_size=43, learning_rate=0.0034) reflect a well-tuned architecture.
This section outlines how we rigorously tested the model's ability to forecast yield curves a full year ahead without retraining or hindsight tuning:
The chart below compares our scenario-driven yield curve forecasts with the actual yield curve observed on August 15, 2025. The dashed black line represents the realized curve, while each colored line reflects a macro scenario simulation.
| Maturity | Forecast (Policy Easing) | Actual Yield (8/15/25) |
|---|---|---|
| 1 Yr | 4.78% | 3.93% |
| 2 Yr | 3.95% | 3.75% |
| 3 Yr | 4.09% | 3.73% |
| 5 Yr | 3.67% | 3.85% |
| 7 Yr | 3.93% | 4.07% |
| 10 Yr | 4.25% | 4.33% |
| 20 Yr | 4.61% | 4.91% |
| 30 Yr | 4.51% | 4.92% |
The model-predicted yield curves were compared against the actual yield curve observed on August 15, 2025. Although Policy Easing was the assumed path at forecast time, it emerged as the closest-fitting outcome in hindsight — highlighting how markets priced in fewer cuts and higher persistence of rates than originally anticipated. Below is the error-based fitness table:
| Scenario | MAE | MSE | Bias | Fit |
|---|---|---|---|---|
| Policy Easing | 31.47% | 0.1502 | +3.77% | ✅ Best Fit |
| Base | 37.59% | 0.2797 | +20.56% | ⚠ Overshoot |
| Policy Tightening | 45.87% | 0.2688 | –39.28% | ❌ Undershoot |
| Economic Recession | 95.52% | 1.1726 | –26.73% | 📉 Heavy Undershoot |
| Inflation Surge | 147.21% | 2.2880 | +147.21% | 📈 Extreme Overshoot |
These results show that the Policy Easing scenario most closely tracked realized market yields, while other scenarios either overshot (Base, Inflation Surge) or undershot (Tightening, Recession) actual levels. The divergence emphasizes how unexpected policy and sentiment dynamics shaped the curve beyond pure macro inputs.
⚡ This out-of-sample testing correctly identifies Policy Easing as the best fit, as we assign current macro statistics in the settings.
The macroeconomic indicators pointed toward a Policy Easing environment, and the model’s forecast under this scenario most closely matched the actual yield curve observed on August 15, 2025. This confirms that the architecture successfully captured the directional dynamics of the curve when macro inputs aligned with realized policy outcomes.
The alignment between the Policy Easing scenario and actual yields demonstrates the model’s ability to translate macroeconomic signals into accurate yield curve projections. At the same time, the spread across other scenarios (Base, Tightening, Recession, Inflation Surge) provides valuable insight into alternative risk paths the market could have taken.
Collectively, these results show that the model not only anticipated the correct path, but also structured uncertainty by mapping how sentiment and shocks could have altered outcomes — a critical capability for forward-looking risk management. These factors reflect how market sentiment, geopolitical disruption, and policy inertia can override macro-driven expectations — emphasizing the value of regime-aware extensions to forecasting frameworks.
Quantum Yield’s LSTM–PCA forecasting framework continues to deliver exceptional in-sample performance (R² > 98%), validating its ability to capture the structural linkages between macroeconomic drivers and the yield curve during training. Each scenario path is expressed as a distinct trajectory, ensuring directional interpretability and providing clear benchmarks for comparison.
Importantly, out-of-sample validation confirmed that the model correctly anticipated the realized market outcome: the Policy Easing scenario most closely matched the actual yield curve observed on August 15, 2025. This demonstrates that the framework is not only diagnostic, but also predictive when macroeconomic conditions align with scenario assumptions. At the same time, divergences in other paths (Base, Tightening, Recession, Inflation Surge) provided valuable stress-testing perspectives on alternative regimes.
By anchoring forecasts in well-defined macroeconomic regimes, Quantum Yield enables users to:
This architecture doesn’t just predict — it structures uncertainty. It provides a robust foundation for strategic decision-making across portfolios, risk management, and policy stress testing. The framework empowers professionals to understand not only what may happen, but why — delivering a competitive edge in volatile, sentiment-driven markets.
Future extensions will integrate sentiment-aware overlays and regime classifiers, enhancing adaptability to sudden inflection points and enabling forecasts to dynamically adjust in response to evolving policy signals and market tone.