Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes
This work addresses a fundamental limitation in stochastic volatility models for domains like finance and climatology, though it is incremental as it builds on existing GP frameworks.
The authors tackled the limitation of stochastic volatility models in producing true posterior distributions by recasting them as hierarchical Gaussian process models with specialized covariance functions. Their Volt and Magpie models significantly outperformed baselines in stock and wind speed forecasting, achieving improvements of up to 15% in predictive accuracy.
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.