arXiv subjects

Florian Ziel

Publications and source records attributed to Florian Ziel.

At least 19 recordsLinked to original sources

arXiv2026

Networked Spatial Effects in European Electricity Price Forecasting

As European bidding zones are highly interconnected by physical transmission lines, spatial influences propagate across neighboring nodes through a network. It is reflected in the day-ahead electricity prices across European bidding zones, as the auction algorithm also uses information beyond each bidding zone's geographic boundary. To capture how this interconnection affects the electricity prices in neighboring bidding zones, we have used a metric graph to map the spatial coverage of information using a well-defined neighborhood measure. We propose the Networked Spatio-Temporal Model (NSTM), which maps irregular spatial nodes into an ordered network, enabling the systematic incorporation of neighborhood information. We implement the NSTM across 39 bidding zones covering the majority of European electricity markets in a high-resolution, streaming-forecasting setup. The model uses autoregressive, cross-hour, and seasonal effects, along with fuel and emission prices and day-ahead forecasts of fundamentals, as interconnected information to predict the day-ahead prices for each bidding zone. A Europe-wide study presented in this paper shows that the NSTM consistently outperforms traditional island-based pure local models. This paper provides a framework that demonstrates the critical role the networked structure plays in propagating information across interconnected markets and its vast implications for day-ahead electricity price forecasting.

stat.AP↗

arXiv2026

Fast Training of Mixture-of-Experts for Time Series Forecasting via Expert Loss Integration

We propose a novel adaptive Mixture-of-Experts (MoE) framework for time series forecasting that enhances expert specialization by incorporating expert-specific loss information directly into the training process. Notably, the overall objective comprises the base forecasting loss and expert-specific losses, allowing expert-level prediction errors to jointly shape training alongside the global forecasting loss. This framework is further combined with a partial online learning strategy, enabling incremental updates of both the gating mechanism and expert parameters. This approach significantly reduces computational cost by eliminating the need for repeated full model retraining. By integrating expert-level loss awareness with efficient online optimization, the proposed method achieves improved learning efficiency while maintaining strong predictive performance. Empirical results across economic, tourism, and energy datasets with varying frequencies demonstrate that the proposed approach generally outperforms both statistical methods and state-of-the-art neural network models, such as Transformers and WaveNet, in forecasting accuracy and computational efficiency. Furthermore, ablation studies confirm the effectiveness of the expert-specific loss integration strategy, highlighting its contribution to enhancing predictive performance.

stat.ML↗

arXiv2026

Energy-Arena: A Dynamic Benchmark for Operational Energy Forecasting

Energy forecasting research faces a persistent comparability gap that makes it difficult to measure consistent progress over time. Reported accuracy gains are often not directly comparable because models are evaluated under study-specific datasets, time periods, information sets, and scoring setups, while widely used benchmarks and competition datasets are typically tied to fixed historical windows. This paper introduces the Energy-Arena, a dynamic benchmarking platform for operational energy time series forecasting that provides a continuously updated reference point as energy systems evolve. The platform operates as an open, API-based submission system and standardizes challenge definitions and submission deadlines aligned with operational constraints. Performance is reported on rolling evaluation windows via persistent leaderboards. By moving from retrospective backtesting to forward-looking benchmarking, the Energy-Arena enforces standardized ex-ante submission and ex-post evaluation, thereby improving transparency by preventing information leakage and retroactive tuning. The platform is publicly available at Energy-Arena.org.

econ.EM↗

arXiv2026

Online Distributional Regression

Large-scale streaming data are common in modern machine learning applications and have led to the development of online learning algorithms. Many fields, such as supply chain management, weather and meteorology, energy markets, and finance, have pivoted toward probabilistic forecasting. This results in the need not only for accurate learning of the expected value but also for learning the conditional heteroskedasticity and conditional moments. Against this backdrop, we present a methodology for online estimation of regularized, linear distributional models. The proposed algorithm combines recent developments in online estimation of LASSO models with the well-known GAMLSS framework. We provide a case study on day-ahead electricity price forecasting, in which we show the competitive performance of the incremental estimation combined with strongly reduced computational effort. Our algorithms are implemented in a computationally efficient Python package ondil.

stat.ML↗

arXiv2026

Probabilistic Forecasting for Day-ahead Electricity Prices, Battery Trading Strategies and the Economic Evaluation of Predictive Accuracy

Electricity price forecasting supports decision-making in energy markets and asset operation. Probabilistic forecasts are increasingly adopted to explicitly quantify uncertainty, typically issued as quantile predictions or ensembles of the full predictive distribution. However, how improvements in statistical forecast quality translate into economic value remains unclear. Battery storage arbitrage in day-ahead markets is a popular application-based benchmark for this purpose. We analyze quantile-based trading strategies (QBTS) and identify two critical flaws: they do not incentivize honest probabilistic forecasting and they ignore the intertemporal dependence structure of electricity prices. We therefore frame battery optimization as a stochastic program based on fully probabilistic forecasts and examine decision quality measurement for risk-neutral and risk-averse settings under different uncertainty models. Our discussion touches both sides of the coin: How reliable is the economic evaluation of forecasting models though (simplified) application studies - and how do improvements in statistical forecast quality for stochastic programs relate to the decision-quality and economic performance? We provide theoretical justification and empirical evidence from a case study on the German electricity market. Our results highlight the pitfalls of ranking forecasting models through battery trading strategies. We conclude with implications for evaluation practice and directions for future research in application-based forecast assessment.

q-fin.ST↗

arXiv2026

Recurrent Neural Networks with Linear Structures for Electricity Price Forecasting

We present a novel recurrent neural network architecture specifically designed for day-ahead electricity price forecasting, aimed at improving short-term decision-making and operational management in energy systems. Our combined forecasting model embeds linear structures, such as expert models and Kalman filters, into recurrent networks, enabling efficient computation and enhanced interpretability. The design leverages the strengths of both linear and non-linear model structures, allowing it to capture all relevant stylized price characteristics in power markets, including calendar and autoregressive effects, as well as influences from load, renewable energy, and related fuel and carbon markets. For empirical testing, we use hourly data from the largest European electricity market spanning 2018 to 2025 in a comprehensive forecasting study, comparing our model against state-of-the-art approaches, particularly high-dimensional linear and neural network models. In terms of RMSE, the proposed model achieves approximately 11% higher accuracy than the best-performing benchmark. We evaluate the contributions of the interpretable model components and conclude on the impact of combining linear and non-linear structures. We further evaluate the temporal robustness of the model by examining the stability of hyperparameters and the economic significance of key features. Additionally, we introduce a probabilistic extension to quantify forecast uncertainty.

stat.ML↗

arXiv2026

Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learning

Precise day-ahead forecasts for electricity prices are crucial to ensure efficient portfolio management, support strategic decision-making for power plant operations, and enable effective battery optimization. However, developing an accurate prediction model is highly challenging in an uncertain and volatile market environment. For instance, although linear models generally exhibit competitive performance in predicting electricity prices with minimal computational requirements, they fail to capture relevant nonlinear relationships. Nonlinear models, on the other hand, can improve forecasting accuracy with a surge in computational costs. We employ a multivariate hybrid neural architecture that combines linear and nonlinear feed-forward neural structures. We then integrate this architecture with a novel partial online learning strategy that combines warm-starting with distinct hyperparameter configurations for each training stage. This strategy, which substantially reduces computational time, constitutes our key contribution. Unlike previous hybrid models, our framework also incorporates forecast combination through Bernstein Online Aggregation (BOA) to further improve forecasting accuracy. Compared with the considered state-of-the-art benchmark implementations in the reported setup, the proposed forecasting method significantly reduces computational cost while delivering better forecasting accuracy (11-12% RMSE and 14-17% MAE reductions). Our results are derived from a six-year forecasting study conducted on major European electricity markets.

cs.LG↗

arXiv2025

A data-driven merit order: Learning a fundamental electricity price model

Electricity price forecasting approaches generally fall into two categories: data-driven models, which learn from historical patterns, or fundamental models, which simulate market mechanisms. We propose a novel and highly efficient data-driven merit order model that integrates both paradigms. The model embeds the classical expert-based merit order as a nested special case, allowing all key parameters, such as plant efficiencies, bidding behavior, and available capacities, to be estimated directly from historical data, rather than assumed. We further enhance the model with critical embedded extensions such as hydro power, cross-border flows and corrections for underreported capacities, which considerably improve forecasting accuracy. Applied to the German day-ahead market, our model outperforms both classic fundamental and state-of-the-art machine learning models. It retains the interpretability of fundamental models, offering insights into marginal technologies, fuel switches, and dispatch patterns, elements which are typically inaccessible to black-box machine learning approaches. This transparency and high computational efficiency make it a promising new direction for electricity price modeling.

stat.AP↗

arXiv2025

Efficient mid-term forecasting of hourly electricity load using generalized additive models

Accurate mid-term (weeks to one year) hourly electricity load forecasts are essential for strategic decision-making in power plant operation, ensuring supply security and grid stability, planning and building energy storage systems, and energy trading. While numerous models effectively predict short-term (hours to a few days) hourly load, mid-term forecasting solutions remain scarce. In mid-term load forecasting, capturing the multifaceted characteristics of load, including daily, weekly and annual seasonal patterns, as well as autoregressive effects, weather and holiday impacts, and socio-economic non-stationarities, presents significant modeling challenges. To address these challenges, we propose a novel forecasting method using Generalized Additive Models (GAMs) built from interpretable P-splines that is enhanced with autoregressive post-processing. This model incorporates smoothed temperatures, Error-Trend-Seasonal (ETS) modeled and persistently forecasted non-stationary socio-economic states, a nuanced representation of effects from vacation periods, fixed date and weekday holidays, and seasonal information as inputs. The proposed model is evaluated using load data from 24 European countries over more than 9 years (2015-2024). This analysis demonstrates that the model not only has significantly enhanced forecasting accuracy compared to state-of-the-art methods but also offers valuable insights into the influence of individual components on predicted load, given its full interpretability. Achieving performance akin to day-ahead Transmission System Operator (TSO) forecasts, with computation times of just a few seconds for several years of hourly data, underscores the potential of the model for practical application in the power system industry.

stat.AP↗

arXiv2025

The role of probabilistic load and renewable prediction in enhancing day-ahead electricity price forecasts

The increasing penetration of renewable energy sources (RES) has amplified volatility in electricity markets, while demand variability continues to challenge system stability. Traditional day-ahead electricity price forecasting (EPF) models rely on point forecasts of load and RES generation, which fail to capture the uncertainty inherent in weather-driven supply and dynamic demand. This study introduces a novel framework that integrates probabilistic forecasts of load, wind, and solar generation into EPF models. Using data from the German EPEX market between 2015 and 2023, we generate quantile forecasts of fundamental variables via historical simulation, conformal prediction and quantile regression, and incorporate them into both parsimonious expert and high-dimensional LASSO-based models. Empirical results show that probabilistic inputs substantially enhance forecast accuracy, reducing root mean square errors by up to 13% compared with point-forecast benchmarks. Notably, extreme quantiles of load and RES forecasts emerge as the most influential predictors, underscoring the importance of rare but system-critical scenarios. These findings demonstrate that accounting for uncertainty in both load and renewables is crucial for reliable electricity price forecasting and offers practical value for system operators, traders, and policymakers navigating renewable integration.

stat.AP↗

arXiv2024

Spatial Weather, Socio-Economic and Political Risks in Probabilistic Load Forecasting

Accurate forecasts of the impact of spatial weather and pan-European socio-economic and political risks on hourly electricity demand for the mid-term horizon are crucial for strategic decision-making amidst the inherent uncertainty. Most importantly, these forecasts are essential for the operational management of power plants, ensuring supply security and grid stability, and in guiding energy trading and investment decisions. The primary challenge for this forecasting task lies in disentangling the multifaceted drivers of load, which include national deterministic (daily, weekly, annual, and holiday patterns) and national stochastic weather and autoregressive effects. Additionally, transnational stochastic socio-economic and political effects add further complexity, in particular, due to their non-stationarity. To address this challenge, we present an interpretable probabilistic mid-term forecasting model for the hourly load that captures, besides all deterministic effects, the various uncertainties in load. This model recognizes transnational dependencies across 24 European countries, with multivariate modeled socio-economic and political states and cross-country dependent forecasting. Built from interpretable Generalized Additive Models (GAMs), the model enables an analysis of the transmission of each incorporated effect to the hour-specific load. Our findings highlight the vulnerability of countries reliant on electric heating under extreme weather scenarios. This emphasizes the need for high-resolution forecasting of weather effects on pan-European electricity consumption especially in anticipation of widespread electric heating adoption.

stat.AP↗

arXiv2024

From day-ahead to mid and long-term horizons with econometric electricity price forecasting models

The recent energy crisis starting in 2021 led to record-high gas, coal, carbon and power prices, with electricity reaching up to 40 times the pre-crisis average. This had dramatic consequences for operational and risk management prompting the need for robust econometric models for mid to long-term electricity price forecasting. After a comprehensive literature analysis, we identify key challenges and address them with novel approaches: 1) Fundamental information is incorporated by constraining coefficients with bounds derived from fundamental models offering interpretability; 2) Short-term regressors such as load and renewables can be used in long-term forecasts by incorporating their seasonal expectations to stabilize the model; 3) Unit root behavior of power prices, induced by fuel prices, can be managed by estimating same-day relationships and projecting them forward. We develop interpretable models for a range of forecasting horizons from one day to one year ahead, providing guidelines on robust modeling frameworks and key explanatory variables for each horizon. Our study, focused on Europe's largest energy market, Germany, analyzes hourly electricity prices using regularized regression methods and generalized additive models.

stat.AP↗

arXiv2024

Assessing the impact of weather-induced uncertainties in large-scale electricity systems

The future energy system will largely depend on volatile renewable energy sources and temperature-dependent loads, which makes the weather a central influencing factor. This article presents a novel approach for simulating weather scenarios for robust large-scale power system analysis. By applying different signal analysis methods, historical weather data is decomposed into its spectral components, processed appropriately, and then used to generate random, self-consistent weather data. In this process, any weather parameters of different locations can be considered, while their respective dependencies are mapped. The added value is demonstrated by coupling with a state-of-the-art large-scale energy system model for Europe. It is shown that the integrated consideration of different weather influences allows a quantification of the range of fluctuation of various parameters - such as the feed-in of wind and solar power - and thus provides the basis for future resilient grid planning approaches.

eess.SY↗

arXiv2024

Multivariate Probabilistic CRPS Learning with an Application to Day-Ahead Electricity Prices

This paper presents a new method for combining (or aggregating or ensembling) multivariate probabilistic forecasts, considering dependencies between quantiles and marginals through a smoothing procedure that allows for online learning. We discuss two smoothing methods: dimensionality reduction using Basis matrices and penalized smoothing. The new online learning algorithm generalizes the standard CRPS learning framework into multivariate dimensions. It is based on Bernstein Online Aggregation (BOA) and yields optimal asymptotic learning properties. The procedure uses horizontal aggregation, i.e., aggregation across quantiles. We provide an in-depth discussion on possible extensions of the algorithm and several nested cases related to the existing literature on online forecast combination. We apply the proposed methodology to forecasting day-ahead electricity prices, which are 24-dimensional distributional forecasts. The proposed method yields significant improvements over uniform combination in terms of continuous ranked probability score (CRPS). We discuss the temporal evolution of the weights and hyperparameters and present the results of reduced versions of the preferred model. A fast C++ implementation of the proposed algorithm is provided in the open-source R-Package profoc on CRAN.

stat.ML↗

arXiv2023

Multivariate Simulation-based Forecasting for Intraday Power Markets: Modelling Cross-Product Price Effects

Intraday electricity markets play an increasingly important role in balancing the intermittent generation of renewable energy resources, which creates a need for accurate probabilistic price forecasts. However, research to date has focused on univariate approaches, while in many European intraday electricity markets all delivery periods are traded in parallel. Thus, the dependency structure between different traded products and the corresponding cross-product effects cannot be ignored. We aim to fill this gap in the literature by using copulas to model the high-dimensional intraday price return vector. We model the marginal distribution as a zero-inflated Johnson's $S_U$ distribution with location, scale and shape parameters that depend on market and fundamental data. The dependence structure is modelled using latent beta regression to account for the particular market structure of the intraday electricity market, such as overlapping but independent trading sessions for different delivery days. We allow the dependence parameter to be time-varying. We validate our approach in a simulation study for the German intraday electricity market and find that modelling the dependence structure improves the forecasting performance. Additionally, we shed light on the impact of the single intraday coupling (SIDC) on the trading activity and price distribution and interpret our results in light of the market efficiency hypothesis. The approach is directly applicable to other European electricity markets.

q-fin.ST↗

arXiv2023

Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions

Aggregated curves are common structures in economics and finance, and the most prominent examples are supply and demand curves. In this study, we exploit the fact that all aggregated curves have an intrinsic hierarchical structure, and thus hierarchical reconciliation methods can be used to improve the forecast accuracy. We provide an in-depth theory on how aggregated curves can be constructed or deconstructed, and conclude that these methods are equivalent under weak assumptions. We consider multiple reconciliation methods for aggregated curves, including previously established bottom-up, top-down, and linear optimal reconciliation approaches. We also present a new benchmark reconciliation method called 'aggregated-down' with similar complexity to bottom-up and top-down approaches, but it tends to provide better accuracy in this setup. We conducted an empirical forecasting study on the German day-ahead power auction market by predicting the demand and supply curves, where their equilibrium determines the electricity price for the next day. Our results demonstrate that hierarchical reconciliation methods can be used to improve the forecasting accuracy of aggregated curves.

stat.AP↗

arXiv2023

Modeling Volatility and Dependence of European Carbon and Energy Prices

We study the prices of European Emission Allowances (EUA), whereby we analyze their uncertainty and dependencies on related energy prices (natural gas, coal, and oil). We propose a probabilistic multivariate conditional time series model with a VECM-Copula-GARCH structure which exploits key characteristics of the data. Data are normalized with respect to inflation and carbon emissions to allow for proper cross-series evaluation. The forecasting performance is evaluated in an extensive rolling-window forecasting study, covering eight years out-of-sample. We discuss our findings for both levels- and log-transformed data, focusing on time-varying correlations, and in view of the Russian invasion of Ukraine.

q-fin.ST↗

arXiv2022

Distributional neural networks for electricity price forecasting

We present a novel approach to probabilistic electricity price forecasting which utilizes distributional neural networks. The model structure is based on a deep neural network that contains a so-called probability layer. The network's output is a parametric distribution with 2 (normal) or 4 (Johnson's SU) parameters. In a forecasting study involving day-ahead electricity prices in the German market, our approach significantly outperforms state-of-the-art benchmarks, including LASSO-estimated regressions and deep neural networks combined with Quantile Regression Averaging. The obtained results not only emphasize the importance of higher moments when modeling volatile electricity prices, but also -- given that probabilistic forecasting is the essence of risk management -- provide important implications for managing portfolios in the power sector.

q-fin.ST↗