Integrating Traditional Statistics and Machine Learning: A Study on SPY Volatility Prediction Based on Conformal Prediction

This article introduces an open-source SPY volatility prediction project that combines GARCH models, Random Forest, and conformal prediction techniques. It explores the complementarity between traditional statistical methods and machine learning in financial market prediction. The core is to compare the performance of three types of models (GARCH(1,1), Random Forest, hybrid model) and introduce conformal prediction to quantify prediction uncertainty.

Volatility prediction is a core challenge in quantitative finance, related to profit and tail risk control. As the world's most traded ETF, SPY's volatility reflects U.S. stock market sentiment. Traditional GARCH models have solid theoretical foundations but their linear structure struggles to capture nonlinear patterns; machine learning methods (e.g., Random Forest) are flexible but need to explore integration with traditional methods. This project innovatively introduces conformal prediction technology to solve the problem of uncertainty quantification.

Comparison of Three Models

1. GARCH(1,1)：A benchmark statistical model that captures volatility clustering effects. Its parameters are interpretable but limited by linear structure.
2. Random Forest：An ensemble learning method that automatically captures nonlinear interactions and excels at handling high-dimensional features.
3. GARCH-RF Hybrid Model：A cascaded structure where residuals are first extracted via GARCH, then used as features input to Random Forest, combining the advantages of both.

Application of Conformal Prediction

Split Conformal Prediction is used to construct prediction intervals. It requires no strong distribution assumptions, ensures marginal validity of coverage probability, and helps evaluate prediction credibility.

Experimental Design

• Data: SPY historical price data, with realized volatility calculated as the prediction target.
• Evaluation Metrics: RMSE (point prediction accuracy), MAE (robust error), coverage rate (actual coverage proportion of intervals), interval width (precision).

Technical Implementation Modules

• Data Acquisition and Preprocessing: Obtain data from Yahoo Finance, calculate log returns and realized volatility.
• GARCH Modeling: Implement GARCH(1,1) using the arch library or statsmodels.
• Feature Engineering: Construct technical indicators, lag features, etc.
• Random Forest Training: scikit-learn regression model.
• Conformal Prediction: Custom Split Conformal logic.
• Evaluation and Visualization: Compare model results and interval coverage.

Research Findings

• Pure machine learning models (e.g., Random Forest) perform well in fitting historical data but are prone to overfitting out-of-sample.
• Hybrid models balance stability and accuracy well.
• Conformal prediction intervals have robust coverage rates and remain effective under model misspecification.

Practical Significance

Provides a complete volatility prediction framework with implementation references for all links from data preprocessing to uncertainty quantification, offering a valuable starting point for quantitative strategy researchers.

Limitations

• GARCH model assumptions may break down in extreme market conditions.
• Machine learning models require large amounts of data and have poor interpretability.
• Hybrid models increase complexity.

Future Directions

• Introduce high-frequency data to calculate realized volatility.
• Try deep learning models such as LSTM and Transformer.
• Explore adaptive conformal prediction to address distribution drift.