Quantifying Uncertainty with a Derivative Tracking SDE Model and Application to Wind Power Forecast Data

TL;DR

This paper introduces a novel SDE-based methodology for modeling forecast errors in wind power data, capturing asymmetric dynamics and providing sharp confidence bands for future predictions.

Contribution

It develops a parametric Itô's SDE framework with time-derivative tracking and an improved diffusion term, including proofs of solution properties and a new likelihood optimization approach.

Findings

Effective modeling of wind power forecast errors

Sharp empirical confidence bands achieved

Framework is agnostic to forecasting technology

Abstract

We develop a data-driven methodology based on parametric It\^{o}'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.