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Quantifying uncertainty with a derivative tracking SDE model and application to wind power forecast data

机译：用衍生性跟踪SDE模型的量化和应用于风电预测数据的不确定性

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We develop a data-driven methodology based on parametric Ito's Stochastic Differential Equations (SDEs) to capture the real asymmetric dynamics of forecast errors, including the uncertainty of the forecast at time zero. 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 by imposing conditions on the time-varying mean-reversion parameter. We develop the structure of the drift term based on sound mathematical theory. A truncation procedure regularizes the prediction function to ensure that the trajectories do not reach the boundaries almost surely in a finite time. 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 a fixed-point likelihood optimization approach in the Lamperti space. Another novel contribution is the characterization of the uncertainty of the forecast at time zero, which turns out to be crucial in practice. We extend the model specification by considering the length of the unknown time interval preceding the first time a forecast is provided through an additional parameter in the density of the initial transition. 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 wind power production forecast error are obtained for the best-selected model.
机译：我们基于参数ITO的随机微分方程（SDE）开发数据驱动方法，以捕获预测误差的实际不对称动态，包括在零时预测的不确定性。我们的SDE框架具有预测，时变平均值参数和改进的状态依赖性扩散项的时间衍生跟踪。通过在时变平均值参数上施加条件，示出了SDE溶液的存在，强唯一性和界限的证据。基于声音数学理论，我们开发了漂移项的结构。截断程序正规化预测功能，以确保轨迹几乎肯定地在有限时间内几乎不达到边界。通过数值优化过程执行通过在原始预测误差空间和LAMPERTI空间中的时刻匹配技术构成的近似似然的推断。我们提出了LAMPERTI空间中的定点似然优化方法。另一个新颖的贡献是在零时的预测的不确定性表征，这反过来在实践中至关重要。我们通过考虑第一次前面的未知时间间隔的长度来扩展模型规范，通过初始转换密度的附加参数提供预测。所有程序都是可靠的预测技术，它们可以在不同的预测提供商之间进行比较。我们将SDE框架应用于模拟历史历史卢瓦圭标准化的风电力生产和2019年12月之间的预测数据。获得最佳选择模型的风电产量预测误差的尖锐经验置信带。

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