TAUNUSSTAR

Methodology: How Our Forecasting Works

Deep dive into our machine learning methodology, model architecture, and validation framework that powers our S&P 500 predictions

S&P 500 AI forecasting model visualization showing machine learning network analyzing financial data, market indicators, and generating future price predictions with expected range forecasts

Machine Learning Explained

What is AI-powered forecasting?

Our system employs a multi-horizon ensemble approach using CatBoost gradient boosting with sophisticated feature engineering and rigorous validation methodologies. The system operates on three distinct prediction horizons (3M, 6M, 12M) to capture different market dynamics and provide actionable signals for various investment strategies.

Unlike traditional investment strategies that rely on fixed rules or human judgment, our machine learning system adapts to changing market conditions through quarterly retraining. We analyze over 100 engineered indicators from 50+ raw data sources simultaneously—far more than any human could track—to identify opportunities and risks across multiple time horizons.

The system doesn't "predict the future" in a magical sense. Instead, it calculates probabilities based on historical patterns using 5-fold time-series cross-validation with walk-forward analysis. When market conditions look similar to past scenarios that led to positive returns, the models flag these as opportunities. When conditions resemble periods before market declines, they signal caution.

Built on robust foundations

Our forecasting system is designed with institutional-grade rigor used by professional hedge funds and quantitative investment firms. We combine cutting-edge CatBoost gradient boosting with time-tested investment principles and rigorous validation methodologies.

Every component—from data quality assurance to feature engineering to model training to signal generation—follows strict validation procedures including 5-fold time-series cross-validation and walk-forward analysis. This ensures our predictions are based on genuine patterns, not statistical flukes or overfitting to past data.

Machine Learning Models
3
Engineered Features
100+
Years of Historical Data
50+
Prediction Accuracy (12M)
97.5%

The Architecture

From data to decisions

Our forecasting pipeline operates in three distinct stages, each designed to extract maximum insight from market data while avoiding common pitfalls.

Data Collection
We gather market prices, economic indicators, and valuation metrics from trusted financial data providers, updated daily.
Feature Engineering
Raw data is transformed into meaningful patterns using technical indicators, statistical measures, and market relationships.
AI Prediction
Three specialized machine learning models analyze patterns to forecast returns over 3, 6, and 12-month horizons.

Market Data

Prices, volatility, valuations

Feature Engineering

100+ technical indicators

AI Models

3, 6, 12-month forecasts

Trading Signal

LONG, MIXED, or CASH

Data Architecture & Processing

Our forecasting system relies on a comprehensive data architecture that combines market data, economic indicators, and valuation metrics. The system processes over 50 different data sources to create a robust foundation for machine learning models. Each data category serves a specific purpose in understanding market dynamics across different economic cycles.

Market Data

The foundation of our analysis consists of real-time market data that captures the immediate sentiment and movements of financial markets. This includes price action, volatility measures, and trading volume data that reflect investor behavior and market stress levels.

  • • S&P 500 daily price data with dividend adjustments for accurate returns calculation
  • • Volatility indices measuring market fear and uncertainty levels
  • • Historical price data spanning over 50 years for robust pattern recognition
  • • Volume and volatility metrics for market stress and liquidity analysis

Economic Indicators

Macroeconomic data provides the fundamental backdrop against which market movements occur. These indicators capture the health of the economy, monetary policy conditions, and broader economic trends that influence long-term market direction.

  • • Interest rates and treasury yields reflecting the cost of money and economic conditions
  • • Money supply growth rates indicating liquidity conditions in the economy
  • • GDP and economic growth data tracking overall economic health
  • • Central bank policy rates and yield curve data for monetary policy analysis

Valuation Metrics

Valuation indicators help determine whether markets are trading at reasonable levels relative to historical norms. These metrics provide crucial context for understanding whether current market levels are sustainable or potentially overextended.

  • • Price-to-earnings ratios for the S&P 500 index
  • • Cyclically-adjusted price-earnings ratios for long-term valuation context
  • • Dividend yield data for income-focused valuation perspectives
  • • Market capitalization relative to GDP for broad market valuation assessment

Data Quality & Processing Pipeline

All data undergoes rigorous processing and quality assurance procedures to ensure reliability and consistency across our models:

  • • Daily frequency standardization to align all data sources on a consistent timeline
  • • Forward-fill procedures for lower-frequency data like monthly economic indicators
  • • Advanced interpolation techniques for handling missing values without introducing bias
  • • Statistical outlier detection using 3-sigma rules with manual verification processes
  • • Automated data validation checks and cross-reference validation against alternative sources
  • • Real-time monitoring for data feed disruptions with automated fallback procedures

Feature Engineering Framework

Raw market data—like prices or interest rates—doesn't tell the full story. We engineer over 100 specialized indicators that capture market momentum, valuation extremes, and economic relationships through sophisticated statistical transformations and technical analysis.

Statistical Transformations

We apply rigorous statistical methods to normalize data and make it comparable across different time periods and market conditions.

# Z-Score Normalization (Expanding Window)
z_score = (value - expanding_mean) / expanding_std
# Percentile Ranking (Expanding Window)
percentile = expanding_rank(value) / total_observations

Applied to returns, volatility, valuation ratios, and economic indicators to create normalized features that work across different market regimes.

1
Momentum Features

Tracking whether markets are trending up, down, or sideways across multiple timeframes:

  • • Rolling sum returns: 21d, 63d, 126d, 252d, 504d
  • • RSI calculations: 14d, 21d, 63d periods
  • • MACD-derived signals with multiple timeframes
  • • Price momentum relative to moving averages

2
Mean Reversion Indicators

Detecting when markets have moved "too far, too fast" and may be due for a reversal:

  • • Distance from moving averages (20d, 50d, 200d)
  • • Bollinger Band positions and squeeze indicators
  • • Overbought/oversold conditions using multiple methodologies
  • • Reversion strength calculations using linear regression slopes

3
Macroeconomic Features

Advanced economic indicators that capture policy and growth dynamics:

  • • Treasury yield curve slopes (2Y-10Y, 3M-10Y)
  • • M2 money supply growth rates (annualized)
  • • GDP growth rate calculations (quarterly annualized)
  • • Federal Reserve balance sheet metrics

4
Advanced Composite Features

Sophisticated indicators that combine multiple data sources:

  • • Buffett Indicator (market_cap / gdp)
  • • Equity risk premium calculations
  • • VIX percentile rankings and volatility regimes
  • • Realized vs. implied volatility spreads

Machine Learning Architecture

CatBoost Implementation

We use CatBoost, an advanced gradient boosting algorithm developed by Yandex, specifically chosen for its superior handling of financial data. CatBoost excels at managing categorical features, preventing overfitting through ordered boosting, and providing robust performance with mixed data types.

The algorithm works by building a series of decision trees, where each subsequent tree corrects the errors of the previous ones. This ensemble approach allows the model to capture complex, non-linear relationships in financial data that would be impossible to model with traditional statistical methods. The "ordered boosting" feature is particularly valuable for time series data, as it prevents the model from using future information to predict past events.

Our configuration uses a conservative learning rate of 0.03, which means each new tree makes only small adjustments to the overall prediction. This slow, steady approach helps prevent overfitting and creates more stable, reliable predictions. The Bayesian bootstrap method adds randomness to the training process, further improving the model's generalization ability.

# CatBoost Model Configuration
model_config = {
# Common parameters across all horizons
'learning_rate': 0.03,
'rsm': 0.7, # Random subspace method
'bootstrap_type': 'Bayesian',
'bagging_temperature': 0.5,
'od_type': 'Iter', # Overfitting detector
'od_wait': 30,
'eval_metric': 'AUC',
'loss_function': 'Logloss',
'auto_class_weights': 'Balanced',
'border_count': 32,
'verbose': False
}
# Horizon-specific parameters
horizon_configs = {
# 3-month horizon configuration
'3M': {
'iterations': 800,
'depth': 4,
'l2_leaf_reg': 15,
'min_data_in_leaf': 25
},
# 6-month horizon configuration
'6M': {
'iterations': 700,
'depth': 4,
'l2_leaf_reg': 18,
'min_data_in_leaf': 28
},
# 12-month horizon configuration
'12M': {
'iterations': 700,
'depth': 4,
'l2_leaf_reg': 20,
'min_data_in_leaf': 30
}
}

3M Horizon

AUC: 75.3%

800 iterations, depth 4

6M Horizon

AUC: 88.4%

700 iterations, depth 4

12M Horizon

AUC: 97.5%

700 iterations, depth 4

Feature Selection Methodology

Feature selection is crucial in machine learning because including too many irrelevant features can hurt model performance, while including too few features might miss important patterns. We employ a sophisticated two-stage selection process to identify the most predictive features while avoiding overfitting:

In the first stage, we train a preliminary model using all available features and measure each feature's importance score. This tells us which features the model finds most useful for making predictions. In the second stage, we apply strict selection criteria to keep only the most valuable features for each time horizon. This process ensures that our models focus on the most relevant market signals while avoiding noise from less important indicators.

# Two-Stage Feature Selection Process
def select_features(X, y, horizon_name):
# Stage 1: Initial training for importance
initial_model = CatBoostClassifier(**params)
initial_model.fit(X, y)
# Stage 2: Apply selection criteria
selected_features = importance_df[
importance_df['importance'] >= min_threshold
]['feature'].head(max_features)

3M Model

Min Importance: 2.0

Max Features: 10

6M Model

Min Importance: 1.2

Max Features: 10

12M Model

Min Importance: 1.0

Max Features: 10

Target Variable Construction

Our binary classification framework creates targets based on the sign of forward returns (direction-only). The default threshold is 0.0% (configurable in `config.yaml`), meaning LONG when the forward return is positive:

# Binary Classification Framework
def create_targets(df, horizon_days, signal_threshold=0.0):
# Forward return aligned with training pipeline
future_returns = df['GSPC'].shift(-horizon_days) / df['GSPC'] - 1
targets = (future_returns > signal_threshold).astype(int)
return targets

Directional classification uses a 0.0% threshold to label up vs. down moves. If you prefer economically filtered signals (post-cost), you can raise the threshold via configuration to require returns above your cost estimate.

Time-Series Cross-Validation

To ensure our models will work in real markets (not just on historical data), we use strict walk-forward validation:

  • Walk-forward testing: Models never see future data during training
  • 5-fold time-series CV: Tested across 5 different historical periods
  • Out-of-sample validation: Final performance measured on unseen data
  • Overfitting prevention: Continuous monitoring to prevent data memorization

Signal Generation & Portfolio Construction

Multi-Model Consensus Mechanism

Rather than relying on a single model, we use a sophisticated "wisdom of the crowd" approach. Three independent models—each trained on different time horizons—vote on market direction. The more models that agree, the larger the recommended position, creating dynamic risk management through conviction-based allocation.

# Multi-Model Voting System
def generate_consensus_signal(model_predictions):
long_votes = sum(1 for prob in model_predictions.values()
if prob > 0.5)
position_sizes = {0: 0.0, 1: 0.3, 2: 0.9, 3: 1.0}
return {
'consensus_signal': 1 if long_votes >= 2 else 0,
'position_size': position_sizes[long_votes]
}
3/3 models bullish:100% invested (STRONG LONG)
2/3 models bullish:90% invested (MODERATE LONG)
1/3 models bullish:30% invested (MIXED)
0/3 models bullish:0% invested (CASH)

This consensus mechanism reduces the impact of any single model being wrong and naturally adjusts position size based on conviction level, creating dynamic risk management through conviction-based allocation.

Risk Management Framework

Our portfolio construction follows institutional-grade risk management principles with comprehensive metrics and systematic position sizing:

Portfolio Construction Rules

  • • Maximum position size: 100% equity exposure
  • • Minimum position size: 0% (cash position)
  • • No leverage or short selling
  • • Transaction cost modeling included

Risk Metrics

  • • Maximum Drawdown: Peak-to-trough decline
  • • Sharpe Ratio: Risk-adjusted returns (target > 1.0)
  • • Sortino Ratio: Downside deviation-adjusted
  • • Value at Risk (VaR): 95% confidence interval

Daily Signal Process

Every trading day, the system follows a structured workflow to generate actionable signals with institutional-grade precision:

  1. 1. Data Collection: Latest market data collected from Yahoo Finance, FRED, and Multpl.com
  2. 2. Feature Engineering: All 100+ indicators computed from fresh data using statistical transformations
  3. 3. Model Predictions: Each model outputs probability scores for positive returns
  4. 4. Signal Conversion: Probabilities above 50% become LONG signals
  5. 5. Consensus Aggregation: Multi-model voting determines position size
  6. 6. Risk Adjustment: Position sizing applied based on conviction level
  7. 7. Execution Timing: Signals delayed by one day for realistic trading

Validation Framework & Model Quality

Rigorous validation is the cornerstone of reliable machine learning models. Our validation framework ensures that our models will perform well in real-world trading conditions, not just on historical data. We use multiple validation techniques to catch potential problems before they affect live trading.

Cross-Validation Methodology

Time series data requires special handling because traditional cross-validation can introduce data leakage. When predicting stock prices, we must never use information from the future to predict the past. Our 5-fold time-series cross-validation ensures that models are trained and tested on chronologically separate data.

Each fold represents a different time period, with the model being trained on earlier data and tested on later data. This mimics real-world trading conditions where we only have access to historical information when making predictions. The walk-forward approach ensures that our validation results are realistic and applicable to live trading.

# Time-Series Cross-Validation Implementation
def time_series_cv_split(data, n_splits=5, test_size=252):
splits = []
total_length = len(data)
for i in range(n_splits):
# Calculate split boundaries
test_start = total_length - test_size * (i + 1)
test_end = total_length - test_size * i
train_end = test_start
train_start = max(0, test_start - test_size * 3)
splits.append({
'train': (train_start, train_end),
'test': (test_start, test_end)
})
return splits

Model Performance Metrics

We use multiple metrics to evaluate model performance, each providing different insights into how well our models work. The Area Under the Curve (AUC) measures the model's ability to distinguish between profitable and unprofitable opportunities. Precision tells us how often our "buy" signals are correct, while recall measures how many profitable opportunities we capture.

# Performance Metrics Calculation
def calculate_classification_metrics(y_true, y_pred, y_proba):
metrics = {
'auc': roc_auc_score(y_true, y_proba),
'precision': precision_score(y_true, y_pred),
'recall': recall_score(y_true, y_pred),
'f1': f1_score(y_true, y_pred)
}
return metrics

Feature Importance Analysis

Understanding which features are most important helps us interpret our models and ensure they're making decisions based on sensible market signals. Our analysis reveals that different time horizons rely on different types of information. Short-term models focus more on momentum and recent price action, while longer-term models emphasize fundamental valuation metrics and economic indicators.

3M Model (Short-term)

Focuses on momentum and recent market action

  1. 1. P/E Ratio Momentum (45.2)
  2. 2. Shiller CAPE Momentum (32.1)
  3. 3. Dividend Yield (28.5)
  4. 4. P/E Z-Score (22.3)
  5. 5. Price Momentum (18.7)

6M Model (Medium-term)

Balances momentum with fundamental valuation

  1. 1. Dividend Yield (52.3)
  2. 2. P/E Ratio (41.8)
  3. 3. CAPE Momentum (35.2)
  4. 4. Money Supply Z-Score (28.9)
  5. 5. Treasury Yield Z-Score (24.1)

12M Model (Long-term)

Emphasizes fundamental and economic indicators

  1. 1. Dividend Yield (61.5)
  2. 2. Money Supply Z-Score (48.2)
  3. 3. GDP Growth Rate (38.7)
  4. 4. CAPE Long-term Momentum (32.1)
  5. 5. Market Cap/GDP Z-Score (28.9)

Risk Considerations & Limitations

While our system employs institutional-grade methodologies and rigorous validation, it's crucial to understand both the capabilities and limitations of any forecasting system:

Model Risk Factors

Overfitting Prevention

  • • Cross-validation with strict temporal ordering
  • • Feature selection based on out-of-sample performance
  • • Regular model validation and performance monitoring
  • • Ensemble approach reduces single-model risk

Data Risk Management

  • • Multiple data source validation
  • • Real-time monitoring for data feed disruptions
  • • Manual verification of major economic releases
  • • Automated fallback procedures for missing data

Known Limitations

Predictive Limitations: Cannot predict black swan events or unprecedented market conditions. Performance degrades during regime changes and is limited to S&P 500 index (not individual stocks).

Technical Limitations: Dependency on data quality and timeliness. Model performance varies by market regime. Transaction costs and execution delays not fully modeled.

Market Regime Risk: Models trained across multiple market cycles (1970-2024) with regular retraining to adapt to changing conditions. Performance monitoring across different market environments.

Regulatory Considerations: Not registered as investment advice. Performance claims based on historical backtesting. No guarantee of future results. Users responsible for their own investment decisions.

System Architecture & Maintenance

Our system includes comprehensive monitoring and maintenance procedures:

  • • Quarterly Retraining: Models updated every 3 months with latest data
  • • Performance Monitoring: Continuous tracking of prediction accuracy
  • • Alert System: Automated alerts for model degradation
  • • Version Control: Automated fallback to previous model version if needed
  • • Stress Testing: Performance evaluation under extreme market conditions

Technical Methodology Disclosure: This comprehensive methodology documentation is provided for institutional investors and quantitative analysts. While our models use advanced CatBoost machine learning techniques, 5-fold time-series cross-validation, and rigorous validation methods, no forecasting system can predict the future with certainty.

Past performance does not guarantee future results. This methodology is provided for transparency and educational purposes only. Always consult with a qualified financial advisor before making investment decisions. The system serves as a foundation for systematic investment strategies while maintaining rigorous risk management standards expected by institutional investors.