Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes

TL;DR

This paper introduces a novel Gaussian process framework for stochastic volatility models, enabling accurate forecasting by conditioning on historical data, with new models outperforming baselines in finance and wind speed prediction.

Contribution

It recasts stochastic volatility models as hierarchical Gaussian processes with specialized covariance functions, enhancing predictive capabilities and extending to multitask settings.

Findings

Volt and Magpie models outperform baselines in stock forecasting

Models significantly improve wind speed prediction accuracy

Framework naturally extends to multitask forecasting

Abstract

A broad class of stochastic volatility models are defined by systems of stochastic differential equations. While these models have seen widespread success in domains such as finance and statistical climatology, they typically lack an ability to condition on historical data to produce a true posterior distribution. To address this fundamental limitation, we show how to re-cast a class of stochastic volatility models as a hierarchical Gaussian process (GP) model with specialized covariance functions. This GP model retains the inductive biases of the stochastic volatility model while providing the posterior predictive distribution given by GP inference. Within this framework, we take inspiration from well studied domains to introduce a new class of models, Volt and Magpie, that significantly outperform baselines in stock and wind speed forecasting, and naturally extend to the multitask setting.