Stealing Accuracy: Predicting Day-ahead Electricity Prices with Temporal Hierarchy Forecasting (THieF)

TL;DR

It is shown that reconciling forecasts for hourly products and 2- to 24-hour blocks can significantly improve accuracy at all levels and the computational cost of reconciliation is comparable to that of predicting hourly prices alone.

Abstract

We introduce the concept of temporal hierarchy forecasting (THieF) in predicting day-ahead electricity prices and show that reconciling forecasts for hourly products and 2- to 24-hour blocks can significantly (up to 13%) improve accuracy at all levels. These results remain consistent throughout a challenging 4-year test period (2021-2024) in the German and Spanish power markets and across model architectures, including linear regression, shallow feedforward neural networks, gradient-boosted decision trees, and a state-of-the-art, pretrained transformer. Given that (i) trading of block products is becoming more common and (ii) the computational cost of reconciliation is comparable to that of predicting hourly prices alone, we recommend using it in daily forecasting practice.

Figures (4)

• Figure 1: Stylized example of the impact of THieF on forecasts at four hierarchy levels (1H, 4H, 8H, 24H). Filled red circles denote reconciled ($\rightarrow$ THieF-XGB) and hollow circles unreconciled forecasts ($\rightarrow$ Base-XGB) obtained using eXtreme Gradient Boosting (see Section \ref{['ssec:XGB']}). Bars represent actual block prices, with light blue indicating the target day, i.e., Sunday, 7.02.2021, in the German EPEX-DE market.
• Figure 2: The summing matrix $\mathbf{S}$ defined in Eq. \ref{['eq:summing_matrix_1']}. Blue blocks denote non-zero elements, and the shading indicates weights ranging from $s_{24}=\frac{1}{24}$ for $\mathbf{S}_{24}$ to $s_1=1$ for $\mathbf{S}_1$.
• Figure 3: German EPEX-DE (top panels) and Spanish OMIE (bottom panels) electricity market data: day-ahead prices (orange or red) and day-ahead load (dark blue) and wind generation (light blue) forecasts. The shaded area marks the first training window, i.e., the data used for training the models to generate forecasts for the first day in the test period (1.1.2021).
• Figure 4: Percentage gains in RMSE from forecast reconciliation in the German EPEX (dark blue) and Spanish OMIE (light blue) markets for block sizes ranging from 1 to 24 hours, separately for each of the four models (left to right) and calendar years (top to bottom).