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

arXiv: https://arxiv.org/abs/2207.06544 · HTML: https://mlsanity.com/paper/2207.06544/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 61 references that are in the map.
- First posted on arXiv 13 Jul 2022.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Automatic Construction and Natural-Language Description of Nonparametric Regression Models](https://mlsanity.com/paper/1402.4304/) (2014)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Differentiable Compositional Kernel Learning for Gaussian Processes](https://mlsanity.com/paper/1806.04326/) (2018)
- [Conditioning Sparse Variational Gaussian Processes for Online Decision-making](https://mlsanity.com/paper/2110.15172/) (2021)
- [Function-Space Distributions over Kernels](https://mlsanity.com/paper/1910.13565/) (2019)
- [Efficient Modeling of Latent Information in Supervised Learning using Gaussian Processes](https://mlsanity.com/paper/1705.09862/) (2017)
- [A Neural Stochastic Volatility Model](https://mlsanity.com/paper/1712.00504/) (2017)
- [The Gaussian Process Autoregressive Regression Model (GPAR)](https://mlsanity.com/paper/1802.07182/) (2018)
- [Financial Applications of Gaussian Processes and Bayesian Optimization](https://mlsanity.com/paper/1903.04841/) (2019)
- [Uncertainty-Aware Lookahead Factor Models for Quantitative Investing](https://mlsanity.com/paper/2007.04082/) (2020)
- [Gaussian Process Volatility Model](https://mlsanity.com/paper/1402.3085/) (2014)
- [Improving Factor-Based Quantitative Investing by Forecasting Company Fundamentals](https://mlsanity.com/paper/1711.04837/) (2017)
- [Scalable Bayesian dynamic covariance modeling with variational Wishart and inverse Wishart processes](https://mlsanity.com/paper/1906.09360/) (2019)

## Built on by (most cited first, 1 of 1)

- [Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo](https://mlsanity.com/paper/2406.04796/) (2024)

## Abstract (arXiv)

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.