Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes
Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes
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DOI：
10.48550/arxiv.2207.06544
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Gregory W. Benton;Wesley J. Maddox;A. Wilson
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文献类型：
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作者：
Gregory W. Benton;Wesley J. Maddox;A. Wilson
一类广泛的随机波动率模型是由随机微分方程组定义的。尽管这些模型在金融和统计气候学等领域取得了广泛的成功，但它们通常缺乏以历史数据为条件来产生真正的后验分布的能力。为了解决这一基本限制，我们展示了如何将一类随机波动率模型重新构建为具有专门协方差函数的分层高斯过程（GP）模型。该 GP 模型保留了随机波动率模型的归纳偏差，同时提供 GP 推断给出的后验预测分布。在此框架内，我们从深入研究的领域中汲取灵感，引入了一类新模型 Volt 和 Magpie，它们在库存和风速预测方面显着优于基线，并自然地扩展到多任务设置。
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.