微分跟踪SDE模型量化不确定性及其在风电功率预测中的应用
Quantifying Uncertainty with a Derivative Tracking SDE Model and Application to Wind Power Forecast Data
摘要：
我们开发了一种基于参数伊藤随机微分方程（SDEs）的数据驱动方法，以捕获预测误差的真实非对称动态。我们的预测框架具有时间导数跟踪的预测，随时间变化的均值回归参数，和改进的状态依赖扩散项。证明的存在性，强唯一性，和有界性的非线性解决方案的原则条件下，随时间变化的均值回复参数。通过在原始预测误差空间和Lamperti空间中的矩匹配技术构建的基于近似似然的推断，通过数值优化程序进行。我们提出了另一个贡献的基础上的固定点似然优化方法在Lamperti空间。所有的程序都是预测技术不可知的，它们可以在不同的预测提供商之间进行比较。我们应用我们的可持续发展框架来模拟2019年4月至12月期间乌拉圭的历史标准化风电产量和预测数据。尖锐的经验置信带的未来风力发电的最佳选择的模型。
英文摘要：
We develop a data-driven methodology based on parametric Itô's Stochastic Differential Equations (SDEs) to capture the real asymmetric dynamics of forecast errors. Our SDE framework features time-derivative tracking of the forecast, time-varying mean-reversion parameter, and an improved state-dependent diffusion term. Proofs of the existence, strong uniqueness, and boundedness of the SDE solutions are shown under a principled condition for the time-varying mean-reversion parameter. Inference based on approximate likelihood, constructed through the moment-matching technique both in the original forecast error space and in the Lamperti space, is performed through numerical optimization procedures. We propose another contribution based on the fixed-point likelihood optimization approach in the Lamperti space. All the procedures are agnostic of the forecasting technology, and they enable comparisons between different forecast providers. We apply our SDE framework to model historical Uruguayan normalized wind power production and forecast data between April and December 2019. Sharp empirical confidence bands of future wind power production are obtained for the best-selected model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
