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

Gregory Benton, Wesley Maddox, Andrew Gordon Wilson
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:1798-1816, 2022.

Abstract

A broad class of stochastic volatility models are defined by systems of stochastic differential equations, and 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-benton22a, title = {Volatility Based Kernels and Moving Average Means for Accurate Forecasting with {G}aussian Processes}, author = {Benton, Gregory and Maddox, Wesley and Wilson, Andrew Gordon}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {1798--1816}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/benton22a/benton22a.pdf}, url = {https://proceedings.mlr.press/v162/benton22a.html}, abstract = {A broad class of stochastic volatility models are defined by systems of stochastic differential equations, and 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.} }
Endnote
%0 Conference Paper %T Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes %A Gregory Benton %A Wesley Maddox %A Andrew Gordon Wilson %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-benton22a %I PMLR %P 1798--1816 %U https://proceedings.mlr.press/v162/benton22a.html %V 162 %X A broad class of stochastic volatility models are defined by systems of stochastic differential equations, and 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.
APA
Benton, G., Maddox, W. & Wilson, A.G.. (2022). Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:1798-1816 Available from https://proceedings.mlr.press/v162/benton22a.html.

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