Forecasting stock return volatility using high-frequency data and robust machine learning ensembles in a Bayesian framework

Project Abstract

Forecasting stock return volatility remains a central challenge for asset pricing, risk management, and trading strategies, especially in the era of high-frequency trading where intraday dynamics exhibit pronounced nonlinearity, clustering, and regime shifts. This study develops a comprehensive framework that integrates high-frequency financial data with robust machine learning ensembles within a Bayesian paradigm to improve volatility forecasts and uncertainty quantification. We first construct a multi-scale feature set from tick-by-tick and minute-interval data, including realized measures, power variations, jump statistics, and microstructure noise-robust estimators, complemented by macroeconomic indicators and sentiment proxies. To address model misspecification and overfitting, we design an ensemble learning system that combines gradient boosting, random forests, support vector machines, and neural networks, with stacking and weighted voting to adaptively allocate predictive importance across regimes. A Bayesian backbone is embedded through hierarchical priors on model parameters, Bayesian model averaging, and posterior predictive checks, enabling coherent uncertainty propagation in volatility predictions and option-implied variance surfaces. We introduce a robust calibration strategy that leverages sequential Monte Carlo and variational inference to update posterior distributions in near real-time as new high-frequency observations arrive, while accounting for market microstructure changes and exogenous shocks. Our methodology explicitly models volatility as a latent process with stochastic volatility dynamics, incorporating asymmetric responses to price moves via tailored loss functions and regime-dependent priors to capture leverage effects and volatility clustering. Empirical analysis utilizes a diverse panel of liquid equities across multiple U.S. and European markets over a ten-year horizon, with out-of-sample tests conducted in forward-looking rolling windows and event-driven scenarios such as earnings announcements and macro surprises. Performance is evaluated against standard benchmarks including GARCH-type models, stochastic volatility models, and non-Bayesian machine learning approaches, using metrics such as root mean squared error, mean absolute scaled error, continuous ranked probability score, and coverage of predictive intervals. We further examine the practical implications for risk management by analyzing value-at-risk and expected shortfall forecasts, hedging effectiveness, and portfolio optimization under model uncertainty. Sensitivity analyses reveal the contributions of high-frequency features, ensemble diversity, and Bayesian calibration to forecast accuracy and calibration quality, as well as robustness to data sparsity and liquidity shocks. The results demonstrate that the proposed Bayesian ensemble framework yields superior probabilistic forecasts of realized volatility, better capture of tail risk, and more reliable uncertainty quantification than traditional methods, particularly during volatile regimes and regime transitions. This work advances the literature on volatility forecasting by harmonizing rich microstructure-informed features with modern ensemble learning under a principled Bayesian umbrella, offering a scalable and interpretable tool for practitioners seeking improved risk measurement, pricing, and strategic decision-making in dynamic financial markets.

Project Overview

What This Project Is About

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A plain-language overview of forecasting stock return volatility using high-frequency data and machine learning ensembles implemented within a Bayesian framework. It explores how very detailed price data gathered at tiny time intervals can improve predictions of how much stock prices swing, and it combines multiple learning methods to be more accurate and reliable.

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The Problem It Addresses

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Stock volatility is a key input for risk management and pricing, but traditional methods can miss quick shifts in market behavior. The project investigates how high-frequency data can capture rapid changes and how combining several learning models within a Bayesian approach can provide better, probabilistic estimates of volatility, especially during turbulent periods.

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Objectives of the Project

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1. Explain what volatility is in simple terms and why it matters for investors and risk managers.
2. Introduce high-frequency data and how it differs from daily data.
3. Describe Bayesian ideas in an accessible way and why they help quantify uncertainty.
4. Show how multiple models can be combined to improve forecasts (ensemble learning).
5. Build a small, practical framework to estimate volatility from real data.

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What You Will Do Step by Step

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1) Learn the basic concepts of volatility, high-frequency data, and Bayesian thinking. 2) Gather suitable stock price data at high frequency. 3) Preprocess data to handle noise and gaps. 4) Implement a few simple volatility models and ensemble methods. 5) Combine models within a Bayesian framework to obtain probabilistic forecasts. 6) Compare forecasts to traditional methods. 7) Interpret results and assess practical usefulness. 8) Document findings and reflect on limitations and future work.

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Expected Outcome

The project should deliver a clear, user-friendly method for forecasting stock volatility with quantified uncertainty, demonstrated on example data, and guidance on when the approach is most reliable. It should also highlight practical implications for traders, risk managers, and researchers.