arXiv CSopen access

FETS Benchmark: Foundation Models Outperform Dataset-specific Machine Learning in Energy Time Series Forecasting

2026 · arxiv_cs

arXiv CS · Papers · License: Open Access · 2026

artificial intelligence, reasoning, knowledge representation

FETS Benchmark: Foundation Models Outperform Dataset-specific Machine Learning in Energy Time Series Forecasting Marco Obermeiera,b,c , Marco Prucknera , Florian Haselbeckb,1 , Andreas Zeiselmairc,1,∗

arXiv:2604.22328v1 [cs.LG] 24 Apr 2026

Julius-Maximilians-Universität Würzburg, Modeling and Simulation Lab, Am Hubland, Würzburg, 97074, Germany b Weihenstephan-Triesdorf University of Applied Sciences, Smart Farming, Am Staudengarten 1, Freising, 85354, Germany c Weihenstephan-Triesdorf University of Applied Sciences, Digital Energy Transition, Hans-Carl-von-Carlowitz-Platz 3, Freising, 85354, Germany

Abstract Driven by the transition towards a climate-neutral energy system, accurate energy time series forecasting is critical for planning and operation. Yet, it remains largely a datasetspecific task, requiring comprehensive training data, limiting scalability, and resulting in high model development and maintenance effort. Recently, foundation models that aim to learn generalizable patterns via extensive pretraining have shown superior performance in multiple prediction tasks. Despite their success and strong potential to address challenges in energy forecasting, their application in this domain remains largely unexplored. We address this gap by presenting the Foundation Models in Energy Time Series Forecasting (FETS) benchmark. We (1) provide a structured overview of energy forecasting use cases along three main dimensions – stakeholders, attributes, and data categories. (2) 54 datasets across 9 data categories are collected and analyzed, guided by typical stakeholder interests. (3) Foundation models are benchmarked against classical machine learning approaches across different forecasting settings, where foundation models consistently outperform datasetspecific optimized machine learning approaches across all settings and data categories – despite the latter having seen the full historic target data during training. In particular, covariate-informed foundation models achieve the strongest performance. Further analysis reveals a strong correlation between predictive performance and the spectral entropy, performance saturation beyond a certain context length and improved performance at higher levels of aggregation, such as national load, district heating demands, and power grid data. Overall, our findings highlight the strong potential of foundation models as scalable and generalizable forecasting solutions for the energy domain, in particular in data-constrained and privacy-sensitive settings. Keywords: Time series foundation models, energy data, forecasting benchmark, machine learning ∗

Corresponding author: [email protected] Email addresses: [email protected] (Marco Pruckner), [email protected] (Florian Haselbeck), [email protected] (Andreas Zeiselmair) 1 These authors contributed equally as joint last authors.

1. Introduction Modern energy systems are undergoing fundamental transformation. Starting from existing centralized structures with a small number of large-scale dispatchable generation units, adapting to predictable load patterns towards high shares of volatile renewable and decentralized generation. This integration demands higher flexibility and demand response, increasing system complexity. To address this, data-driven approaches are key for optimized operation and planning of energy infrastructures [1]. A key component of these is the anticipation of upcoming system states – be it from a market, grid, or system stability perspective. Eventually, accurate time series forecasting plays an essential role in the digitalized energy system of the future. For example, traders can optimize their market positions using precise load and generation forecasts, grid operators need reliable predictions to determine whether a power plant curtailment is necessary to maintain grid stability, and balancing authorities want to estimate their ancillary service needs [2, 3]. In recent years, machine learning-based prediction models have emerged as state-ofthe-art approaches for energy data forecasting [4, 5, 6, 7]. Despite their good prediction performance when optimized for specific energy forecasting tasks, employing machine learning-based approaches leads to several challenges. Many energy systems constitute critical infrastructure, making most energy time series data highly sensitive and thus limiting their availability [8]. Furthermore, current energy systems and markets are fractured in their organizational structure, driven by unbundling requirements, market regulations, and the increasing decentralization of assets, which leads to energy data silos that are not accessible for cross-application use cases. Additionally, many newly deployed energy assets, particularly in the rapid upscaling of renewable energy, frequently lack sufficiently long historical records required for training [9, 10]. The global transformation of the energy system further reinforces the challenge of changing data distributions, requiring recurring model updates [11, 12]. In general, niche applications or forecasting for small scale energy asset often do not justify the effort required for specially trained models. These limitations motivate the development of forecasting approaches that need less task-specific training data, generalize across datasets, and remain stable under distribution shifts. Time series foundation models (TSFMs) have recently gained significant attention in the machine learning community. In particular, Chronos [13] in 2024 attracted attention by adapting existing language model architectures through minimal modifications – requiring only tokenization via scaling and quantization – and demonstrating strong zero-shot performance across diverse domains including finance, healthcare, nature, retail, mobility and energy [13, 14]. Since then, general-purpose benchmarks such as GIFT-EVAL [15] and FEV-Benchmark [16] have adopted similar domain coverage to systematically compare the growing number of TSFMs. By learning generalizable representations from large and diverse pretraining datasets, these models often achieve competitive performance on previously unseen data in zero-shot settings, i.e., without any task-specific training, and thus potentially providing large benefits for energy forecasting. A detailed description of TSFM architectures and modeling approaches is provided in Section 2 (Related Work). Recent works have begun to explore TSFMs for specific energy use cases. Meyer et al. [17] benchmark TSFMs for household load forecasting and find that zero-shot models can match trained-from-scratch Transformers, particularly with longer context, yet the study is limited to univariate settings without covariates or classical machine learning

baselines. Hornek et al. [18] evaluate TSFMs for electricity price forecasting across five European markets and report that task-specific machine learning methods consistently outperform all tested TSFMs in zero-shot mode – again without considering covariates or fine-tuning. Simeone [19] assesses TSFMs for energy load forecasting on a single dataset without machine learning baselines or covariate support. Ferdaus et al. [20] provide a structured review of foundation models for clean energy forecasting but do not conduct a dedicated benchmark. While these studies provide valuable first insights, they each focus on single energy use cases, consider only univariate forecasting, and omit either classical machine learning comparisons or covariate-informed and fine-tuned settings. Despite the general success and the potential benefits of TSFMs, multiple gaps in terms of their application on energy data exist in current research. General-purpose benchmarks treat energy as a single category among many domains, lacking the granularity to determine in which energy use cases TSFMs perform better or worse than task-specific models such as random forests or XGBoost. As shown above, recent domain-specific studies focus on individual energy use cases with narrow dataset coverage and do not include newer models, particularly those supporting covariate forecasting, nor do they systematically compare against classical machine learning baselines. Hence, there is a lack of a comprehensive benchmarking of TSFMs on energy data that include univariate and covariate approaches, zero-shot and task-specific fine-tuning settings as well as a comparison with state-of-the-art classical machine learning-based methods trained task-specifically. In this work, we address these research gaps by empirically investigating the potential of TSFMs to overcome the key challenges of energy data forecasting identified above. For this purpose, we introduce the FETS (Foundation models for Energy Time Series) benchmark, comprising a diverse set of energy-related data as well as foundation models and classical machine learning approaches. Specifically, we make the following contributions: • Leveraging a representative collection of openly available energy datasets we provide as a contribution of this paper. • We systematically assess recent TSFMs across multiple settings such as the forecasting horizon under both zero-shot and fine-tuned conditions. • We further compare these TSFM approaches with specifically trained machine learning predictors (i.e., random forest and XGBoost), which can be considered the state-of-the-art in energy forecasting. • As a further contribution, we analyse in detail the effects of certain parameters of TSFMs on downstream prediction performance. Thus, our findings provide a comprehensive empirical assessment of foundation models for energy time series forecasting, including their strengths and limitations across diverse settings, offering guidance for real-world energy applications. The paper follows a hybrid structure combining the IMRaD convention [21] with the CRISP-DM methodology [22]. Section 2 reviews related work, followed by energy forecasting use cases (Section 3) and the materials and methods (Section 4) covering the dataset collection, evaluated models, and evaluation setup. Benchmark results are presented in Section 5 and discussed separately in Section 6, before Section 7 concludes with key findings and future deployment directions.

2. Related Work In the energy domain, forecasting has traditionally been addressed using statistical approaches accounting for temporal patterns such as ARIMA and machine learningbased methods for tabular data, e.g., random forests and gradient boosting techniques [3, 8]. Comprehensive reviews of electricity price forecasting established early on that the heterogeneous statistical properties of energy time series – spikes, mean reversion, calendar effects – preclude a single dominant model class, motivating dataset-specific tuning and ensemble strategies [23]. As a consequence, practical energy forecasting pipelines are typically built around careful, domain-specific feature engineering – temperature and weather covariates, calendar and holiday indicators, lagged target values, and recency effects – combined with comparatively small, well-regularized models. Lessons from the Global Energy Forecasting Competitions (GEFCom) [24] confirmed that such feature engineering often outweighs architectural complexity, with gradient boosting and quantile regression emerging as strong probabilistic baselines. In line with these findings, Gradient Boosted Trees like XGBoost dominate recent energy forecasting competitions [25, 4, 5], while random forest remains a robust, stable, and simple baseline widely adopted in practical applications due to its minimal tuning requirements and interpretability [26]. Large-scale empirical comparisons further report that such compact, task-specifically tuned tree ensembles remain highly competitive with task-specific deep learning architectures, as the limited historical data typical of individual energy forecasting tasks favor small, low-variance models with strong inductive biases and hand-crafted features over larger, data-hungry architectures [27]. Together, these findings establish XGBoost and random forest – combined with energy-specific feature engineering – as the natural task-specific baselines for evaluating generalist forecasting approaches in the energy domain. Building on these developments, a new class of models has emerged that goes beyond task-specific training – Time Series Foundation Models (TSFMs). 2.1. Time Series Foundation Models TSFMs as well as tabular foundation models have emerged as a new paradigm in time series and tabular data forecasting in general. TSFMs are typically large sequential deep learning based models pretrained on large volumes of diverse real-world and synthetic time series data. Similar to tokenization in natural language processing, an input sequence is divided into fixed-length patches (e.g. 32 timesteps), each transformed into a learned embedding vector. During pretraining, models learn sequential dependencies between these embeddings, often through masked prediction tasks, with the objective of learning generalizable patterns transferable to previously unseen data. Similar principles have recently been proposed for tabular foundation models, which also aim to retrieve transferable representations via pretraining on large and diverse real-world and synthetic data. Hence, after pretraining, TSFMs and tabular foundation models enable downstream forecasting on unseen data, often achieving a good performance in zero-shot and few-shot settings, respectively. While sharing similar pretraining strategies, current foundation models differ regarding their underlying architectural design and modeling assumptions. Several approaches leverage transformer-based sequential models operating on patch embeddings of the time series, e.g., Chronos-2 [14], TimesFM [28], and Moirai2 [29]. Further stateof-the-art approaches are FlowState [30], leveraging state space models, as well as TiRex

[31] building upon an xLSTM-based architecture [32]. For tabular data, TabPFN2.5-TS [33, 34] employs a transformer-based prior-data fitted network. Further distinction between these state-of-the-art approaches lies in the forecasting modes they support, i.e., univariate forecasting predicting a single time series without additional information, covariate-informed forecasting incorporating auxiliary features, and multivariate forecasting jointly modeling multiple related time series. While FlowState and TiRex currently only support univariate forecasting, the further above-mentioned methods also allow to include covariates, which might be beneficial for energy forecasting. Figure 1 shows a schematic example of uni- and covariate zero-shot forecasting. In univariate mode, the model input consists of a segment of the target time series (the context), and the model output comprises a configurable set of forecast quantile trajectories (the horizon). In covariate mode, the inputs are extended with covariates, such as weather forecasts or holiday indicators, allowing to account for dependencies between the target and covariates, e.g., via cross-attention mechanisms. Historical Data

Model Forecast

Uncertainty (10%-90%)

Forecast Start

Value

Actual Values

40 20 0 Context

Horizon

Covariates

Covariate 1 (e.g., Temperature Forecast)

Covariate 2 (e.g., Wind Speed Forecast)

1 0.5 0

Time Figure 1: Zero-shot time series forecasting schematic for univariate and covariate modes: The upper panel shows historical data (blue, 7 days context), model forecast with median (red dashed, 1 day horizon), 10%-90% uncertainty interval (red shaded), and actual values (green). The lower panel displays optional covariates (blue) that are used as additional input features in covariate mode across the same time axis.

2.2. Benchmarks and Energy-Specific Applications To compare the prediction performance of these foundation models, multiple generalpurpose benchmarks such as GIFT-EVAL [15] and FEV-Benchmark [16] have been published. However, these benchmarks show limited coverage of the energy domain, with GIFT-EVAL only including three energy-related datasets and FEV-Benchmark providing data for aggregated country and household loads, electric price forecasting, and solar as well as wind production forecasting [35]. A complementary direction is pursued by TS-Arena [36], a live forecasting platform with a pre-registration protocol that evaluates models on genuinely unseen future data to eliminate train–test contamination by design,

with an initial application focus on the energy sector; however, it currently provides neither a systematic comparison against classical machine learning baselines such as XGBoost or random forest, nor support for covariate-informed forecasting. As already discussed in the introduction, recent works also explore TSFMs for energy data, focusing on individual use cases such as household load forecasting [17], electricity price forecasting [18], univariate energy load forecasting [19], and clean energy forecasting reviews [20]. These contributions provide first insights into the applicability of TSFMs in energy forecasting, but each concentrates on a single energy use case and typically omits covariate-informed modes, fine-tuning, or comparisons against classical machine learning baselines. Building on this, our FETS benchmark differs from prior work as follows: • Unlike the general-purpose benchmarks GIFT-EVAL [15] and FEV-Benchmark [16], which treat energy as one of many domains, we organize the evaluation along stakeholder-driven energy use cases and assemble 54 datasets across 9 energy-specific data categories. • Unlike energy-specific TSFM studies [17, 18, 19], each restricted to a single use case in univariate zero-shot mode, we evaluate covariate-informed TSFMs such as Chronos-2 [14] across diverse energy use cases under both zero-shot and fine-tuned conditions. • Unlike TS-Arena [36], which lacks classical baselines, covariate support, and finetuning, we benchmark against task-specifically tuned XGBoost and random forest as the de facto state-of-the-art in practical energy forecasting. To the best of our knowledge, this provides the first systematic, use-case-differentiated evidence on where foundation models surpass established baselines in energy forecasting, and where dataset-specific machine learning remains the stronger choice. 3. Forecasting Use Cases in the Energy Sector While general-purpose benchmarks treat energy as a single domain, energy data in fact covers a wide range of specific subdomains itself. To allow for a more fine-grained analysis of TSFMs on energy data, we propose an energy-specific taxonomy that clusters datasets by representative fields of current forecasting applications, sub-divided by data categories, stakeholders, and forecast attributes as depicted in Figure 2. Spanning a tree of involved parties, energy applications, and time series characteristics, the respective leafs reflect existing dimensions to be considered. Some leaf-level examples are specific to the European and German market, but the overall structure is broadly transferable. The forecast attributes shown extend those discussed in Ferdaus et al. [20]. The introduced energy stakeholders are derived from the ENTSO-E market role definitions [37] and abstracted to ensure transferability to energy markets beyond Europe, following the stakeholder categorization discussed in Antonopoulos et al. [3]. Data categories reflect the energy sectors electricity, heat, and mobility [38] that come with specific requirements in forecasting respective time series. The electricity domain stands out, as it plays a central role in a future, fully carbon-free energy system, [2], covering generation, load, market, system services and grid time series. Each forecast can be characterized by

attributes such as horizon (long-term to real-time), grid level (transmission to low voltage), and spatial aggregation (national to individual asset). Forecast attributes introduce the technical dimension, covering temporal data resolution as well as forecasting horizons, external influences, addressed grid levels, and finally regional or type aggregation levels [20]. Trader

Grid

Retailer

Op. Balance

Prod-

Resp.

ucer

Op.

Balancing

Stakeholder

Market

Service

Load

District

System

Con-

Op.

sumer

Long

Mid Short

Heat

Mobility

Process

Real-

Heat

Space

Heat

time

Horizon

Energy Forecasts

Transmission

Wind

Data Categories Gener-

Battery

Dispatch.

15 min

ation

Forecast Attributes

1 h

Nondisp.

Holi-

Load

Industry

Grid

Aggregation

Market

System

Export

Day Ahead

Influences

National

days Import

Household

Temporal

5 min

Electricity

HV MV

Resolution Gas

Grid Level

Cluster

IndiLocal

Policy

vidual Region Price

Weather

mFRR

Intraday reBAP

FCR

aFRR

Figure 2: An overview of energy forecasts from different perspectives and dimensions. It constitutes a synthesis of an abstracted interpretation of ENTSO-E market role definitions [37], and forecast attributes derived from Ferdaus et al. [20], common energy balances on a state or national level [38], with aggregated nodes summarizing consumption and production sectors, as well as own considerations.

We can further link each energy system stakeholder to typical data categories of interest, which we show in Table 1. The tasks we consider focus on short-term forecasting applications, which are particularly relevant to operational planning and often subject to challenges such as non-stationarity, making them a promising application domain for TSFMs in the near future. Table 1: Stakeholder interests in energy forecasts with focus on short-term applications Stakeholder

Role / task related to forecasts

System Operator

Real-time grid balancing, frequency control, and system security (intraday to day-ahead).

Grid Operator

Congestion forecasting to anticipate line/transformer overloads, enabling pre-emptive switching operations, redispatch requests, and real-time monitoring. Minimizing imbalance costs through portfolio balancing (15-min to dayahead).

Balance Party

Responsible

Trader

Intraday and day-ahead trading, arbitrage, and position optimization.

Producer

Unit commitment and dispatch optimization (5min ahead to day-ahead).

Energy Supplier

Short-term procurement and balancing group management for retail customers. Day-ahead and intraday market clearing and price formation.

Market Operator

Balancing Provider

Service

Consumer (industry commercial)

Consumer (residential with HEMS) Metering Point Administrator / Data roles

Bidding strategies for frequency restoration reserves (aFRR, mFRR). Demand response, peak shaving, and intraday procurement for flexible loads. Home energy management, optimal scheduling of flexible loads and storage. Real-time data validation and operational monitoring of metering infrastructure.

Typical forecasted targets (data catagories) Aggregated load, non-dispatchable generation (wind, PV), balancing reserve activation (aFRR, mFRR), grid power flows. Regional load, distributed nondispatchable generation, mobility (EV peaks), heat (heat pumps), grid line flows, grid components/assets, i.e., network transformer load. Portfolio load, non-dispatchable generation, balancing energy prices (reBAP), imbalance volumes, balancing discrepancies, short-term/ID prices. Market prices (day-ahead, intraday), load patterns, non-dispatchable generation, cross-border flows. Plant-specific non-dispatchable generation (wind, PV), market prices, balancing service activation. Customer load, mobility (EV charging), heat (heat pumps), market prices, distributed generation. Aggregated load, non-dispatchable generation, cross-border capacity, market bid/offer curves. Balancing reserve activation, system frequency, market prices for reserve energy, flexible assets. Site load, on-site non-dispatchable generation (PV), process heat, mobility (fleet), market prices. Household load, heat (heat pump), mobility (EV charging), rooftop PV, battery storage, market prices. Metered load, mobility (EV), heat (heat pumps), anomaly detection, data volume validation.

4. Materials and Methods In this work, we provide a systematic assessment of TSFMs on a comprehensive set of energy forecasting data. In Figure 3, we provide an overview of the main components of our study. First, we consider representative datasets from different categories of the energy sector following the above-described taxonomy, allowing both general and task-specific conclusions. Second, we evaluate a wide range of prediction models including TSFMs as well as classical machine learning-based state-of-the-art comparison partners, across the three TSFM forecasting modes: univariate zero-shot, covariate zero-shot settings, and taskspecific fine-tuning regimes. Third, we define a consistent evaluation framework allowing for a fair comparison and further analysis of the behavior of the employed approaches. In this section, we describe the components of this benchmark in detail, beginning with the selection and preparation of the datasets, followed by the forecasting models, and finally the evaluation setup. Data

Models

Evaluation

Non-dispatch Generation PV

Univariate

NRMSE

Market Dayahead

Chronos-2

Flowstate

TimesFM

Tirex

Covariate Heat Heat Demand

Chronos-2 TimesFM

Mobility EV Load Data Category XY ...

Covariates: Hist. Weatherforecasts (Temp., Wind, Radiation) Calendar (Hour, Day, Holiday)

TabPFNTS

Training/Finetuning Chronos-2

XGBoost

Median of each Data Category Spectral Entropy vs. Forecast Performance Sensitivity Analyses: Context, Horizon, Aggregation Level

Random Forest

Ó Benchmark Settings: Context Length: 672 – 8000 (1w – 12w @ 15min) Forecast Horizon: 96 – 288 (1d – 3d @ 15min) Rolling Windows: 35 windows

Figure 3: Benchmark architecture overview: Datasets are fed into three deployment modes with covariates as additional inputs. Models are evaluated across multiple perspectives with consistent benchmark settings.

4.1. Selected Datasets Based on the data categories that are typically of interest for stakeholders (see Table 1), we selected a representative set of datasets for this study, presented in Table 2. Our dataset selection follows four main criteria: (1) open availability, (2) recency with a preference for datasets covering timeseries data from 2022 onwards, (3) domain relevance based on citation count and market size, and (4) category coverage across all segments identified in Table 1. For each dataset and benchmark mode, representative target subsets are used (partly randomly selected; see Table A.5). Each dataset is assigned to the data categories given in Figure 2. The general data section contains datasets that could be assigned to multiple data categories or comprise general feature sets. Historical weather forecasts and calendar data serve as covariates across all forecasting tasks. Typical meteorological features include temperature (2 m height), wind speed (at 80 m, 120 m, and 180 m hub heights), shortwave radiation, and direct radiation. Temporal features comprise cyclic encodings of hour, minute, weekday, day, and month using sine and cosine transformations to preserve periodicity. Calendar features include binary indicators for weekends and public holidays derived from state-specific holiday calendars. Most datasets originate from the largest European electricity markets, with additional datasets from Asia and the United States. Table 2: Comprehensive overview of all datasets used in this study, categorized according to Figure 2 and providing references besides a general description and outlining their usage in our comparative study. Category & Dataset

Description

Benchmark Usage

Ref.

Holiday and temporal features (DE, FR, NL, UK, CN, CH, CA, Bavaria, ...) Load, generation, and market data for European countries

All benchmark modes; required by TabPFN [33][34]

[39]

Country-level load, solar, wind, fossil generation, dayahead spot market prices

[40]

EV charging at large office parking lot, Netherlands Public EV charging stations across Germany Urban EV charging demand dataset, Shenzhen, China Domestic EV chargepoint analysis data, United Kingdom

Aggregated EV charging power forecasting Aggregated EV charging (50–25000 EVs) Urban-scale EV charging demand forecasting Residential EV charging forecasting

[41]

Heat pump smart meter data with inspection protocols Heat Grid Flensburg Network data of the district heating system for the city of Flensburg from 2020–2024 Non-Dispatchable Generation Energy Forecasting ComHybrid wind and PV forecasting petition competition, UK

Heat pump electricity demand forecasting District heating forecasting with historical weatherprediction

[45]

General Data Calendar Features

ENTSO-E Transparency

Mobility Data Office EV Parking (NL) Mobilithek UrbanEV UK Department Transport Heat Data HEAPO

for

Hill of Towie Wind Farm PV Hong Kong DE/FR/DK Power Solar

Onshore wind farm active power measurements, Scotland High-resolution rooftop PV generation, 3-year, China Country-level solar generation for DE, FR, DK

[42] [43] [44]

[46]

Wind park, PV cluster, and [47] hybrid wind+PV forecasting 15-min wind farm power [48] forecasting Single rooftop PV system [49] forecasting National solar generation [40] forecasting Continued on next page

Table 2 – continued from previous page Description Benchmark Usage Onshore and offshore wind generaNational wind generation tion for Germany forecasting California CAISO 5-min resolution aggregated load Aggregated solar forecastdata for California (CAISO) ing (US market) Dispatchable Generation ENTSO-E Germany Fossil gas and hard coal generation Dispatchable generation for Germany forecasting 5-min resolution aggregated generBattery storage dispatch California CAISO ation data for California (CAISO) forecasting (US market) Load Data KIT Company Load Electricity consumption of 28 GerIndustrial and commercial man companies (15-min) load forecasting Industrial VEA Profiles 5359 industrial load profiles Industrial load forecasting Country-level load for Germany National electricity demand DE/FR Power Load and France forecasting California CAISO 5-min resolution aggregated load Aggregated load forecasting data for California (CAISO) (US market) Residential Load TSFM Household BenchHousehold electricity load with Short-term household load mark foundation model benchmark forecasting HTW Berlin Households Representative load profiles at 1Individual and aggregated second resolution household load (2–80 households) Lower Saxony HouseSingle-family house and heat pump Individual household deholds load profiles mand with/without PV Market Data reBAP balancing energy price accross conBalancing energy price foretrol areas for Germany casting Day-Ahead Prices EPEX day-ahead auction prices Day-ahead electricity price (DE-LU) forecasting Intraday Prices Continuous intraday market prices Intraday price forecasting Locational marginal prices (NP15, Electricity price forecasting California CAISO SP15, ZP26) (US market) Grid Data 50Hertz Line Power Transmission line power for highHigh-voltage line power voltage lines flow forecasting Bayernwerk MV Grid Medium voltage grid feed-in and MV grid load and feed-in consumption forecasting LV Grid Feeders (200) Real-world energy data of 200 lowLow-voltage grid load forevoltage grid feeders with metadata casting Balancing Services aFRR Germany Automatic frequency restoration reaFRR activation forecastserve activation ing (positive/negative) mFRR Germany Manual frequency restoration remFRR activation forecastserve (TenneT TSO) ing (positive/negative) NRV Saldo Network control area balance for NRV balance forecasting Germany Weather & Calendar Data Open-Meteo API Historical and forecast weather Weather covariates for all data forecasting tasks High-resolution weather model High-resolution weather DWD ICON-D2 (2.2 km, Central Europe) features for Germany/Europe Dataset DE Power Wind

Ref. [40] [50, 51]

[40] [50, 51]

[52] [53] [40] [50, 51]

[17] [54]

[55]

[56] [40] [57] [50, 51]

[58] [59] [60][61]

[62] [62] [62]

[63] [64]

4.2. Data Preparation Since 15-minute settlement intervals are the standard for the most of the European and Asian energy markets, all time series are resampled to this resolution. California (CAISO) datasets constitute an exception and are retained at their native 5-minute resolution to reflect US market practices. Datasets with lower native resolution (for example, hourly data) are upsampled by duplicating values within each hour. For datasets with mixed resolutions, such as historic segments at hourly resolution and more recent segments

at 15-minute resolution, both resolutions are retained keeping the original time series. Additionally, some time series exhibit varying resolutions with outliers or data gaps resulting in irregular sampling intervals. Mobility datasets typically store individual charging events in a tabular format, recording start time, end time, energy delivered (in Wh or kWh), and, if available, maximum charging power per charging point. For datasets lacking explicit power specifications, a standard charging power of 11 kW was assumed, in line with the prevalent three-phase Type 2 AC charging standard in Europe [65]. From these event-based records, continuous time series were constructed by converting start time, charging power, and energy delivered into aggregated load profiles at 15-minute resolution. Table A.5 provides a statistical overview of all datasets, including sample size (N ), temporal resolution, coefficient of variation (CV), share of negative and positive values, and the Forecastability Index ϕ, which is formally introduced and described in Section 4.4. The collection spans a wide range of signal characteristics, with CV values typically ranging from ≈ 0.18 for stable aggregated signals such as system load to values above 2 for highly volatile signals such as balancing services (CV ≈ 1.7–12) and individual residential loads (CV ≈ 0.9–2.4), with district heat (CV ≈ 0.57) positioned in between. Extreme CV values occur for signals with a near-zero mean, such as low-voltage feeders combining local consumption and PV feed-in (CV ≈ 27), where consumption and generation largely cancel out on average; in such cases, the CV becomes disproportionately large and no longer reflects the effective amplitude of the signal. More generally, a high CV indicates strong amplitude variation relative to the mean, but does not necessarily imply low predictability – a distinction captured by ϕ, which reflects structural regularity independently of the mean. Temporal resolutions mostly lie at 15 minutes, with a few datasets at 5 minutes, 30 minutes, or 1 hour. Negative values – typical for signed quantities such as grid balancing errors or battery charging power – occur primarily in balancing services, some grid feeders, and dispatchable battery profiles. All datasets, except for a small number with license restrictions, are released by the authors in a preprocessed form. 2 4.3. Selected Forecasting Models For our systematic assessment of TSFMs for energy data forecasting, we further select a diverse set of models due to multiple criteria, see Table 3. Only models with openly available weights and code are included. We further aim to include TSFMs that differ in terms of their underlying architecture, i.e., transformer-, state space-, and xLSTM-based approaches. Beyond that, the selected models should allow to evaluate univariate and covariate-informed settings as well as a task-specific fine-tuning, which is currently a limitation for many approaches. The multivariate mode is excluded due to its minimal improvement potential compared to the univariate setup, as shown in the Chronos-2 paper by Ansari et al. [14] (Fig. 10a, p. 22). Finally, we consider performance on the general-purpose benchmarks GIFT-Eval [15] and FEV-Bench [16] as selection criterion.

Available at: 10.5281/zenodo.19418721 [66].

Table 3: Overview of the forecasting models used in this study, including references and the forecasting modes we employ. Model

Type

Ref.

Mode

Additional Information

Chronos-2

Foundation Model Foundation Model Foundation Model

[14]

Version 2.2.2

[28]

Univariate, Covariate, Finetuning Univariate, Covariate

[31]

Univariate

FlowState

Foundation Model

[30]

Univariate

TabPFN-TS

Foundation Model

[33][34]

Covariate

Random Forest

Bagging Ensemble Gradient Boosting

[26]

Training

[25]

Training

TimesFM TiRex

XGBoost

Version 2.0.0, does not yet support finetuning Version 1.4.0, does not yet support covariates and finetuning Version -r1.1, does not yet support covariates and finetuning TabPFN-TS with TabPFN2.6 [33], Version 7.0.1 (TabPFN), Version 1.0.7 (TabPFN-TS) Version 26.2.0, Built with cuml-cu12 Version 3.1.1, Built with xgboost python package

Most foundation models use attention-based transformer architectures [67], including Chronos-2 [14], TimesFM [28], and TabPFN-TS [34, 33]. To evaluate architectural diversity, we include FlowState [30], a state space model [68] based on S5 [69], and TiRex [31], which uses an xLSTM-based architecture [32]. While TiRex and FlowState only support univariate forecasting, TimesFM and Chronos-2 are considered both in univariate and covariate-informed settings, whereas TabPFN-TS is used in covariate mode. To assess potential benefits of a domain-specific adaptation, we additionally fine-tune Chronos-2 on the respective training datasets. In Figure 4, we provide an overview of the data splits employed for our comparative study. Chronos-2 is fine-tuned using the hyperparameters listed in Table A.6 on the same fixed evaluation block as used in the univariate and covariate modes. All remaining time steps of each dataset constitute the training block, whose length therefore varies per dataset. The training block is segmented into sliding windows of identical context length C and forecast horizon H for each experimental setting, with a window overlap of 75%. A main question of our study is how TSFMs perform compared to state-of-the-art models in energy forecasting, which is why we include the classical machine learning-based approaches XGBoost and random forest – the dominant task-specific baselines in the energy domain as outlined in Section 2. Both are trained task-specific, employing the subsequent pipeline following established practices in the literature [70, 71, 5]: 1. Automatic lag selection: Generation of candidate lagged features and selection of the most informative lags based on SHAP importance scores. 2. Feature selection: Retention of the top 50 features from lagged features and engineered features using SHAP values to reduce dimensionality and prevent overfitting. 3. Hyperparameter optimization: Bayesian optimization with Optuna, using 250 trials per quantile and validation performance in terms of the mean squared error for the median and the pinball loss for the other quantiles as objective. An overview of the hyperparameters considered and their ranges is given in Table A.6.

4. Final retraining: Training of the final model on the full training set using the selected features and optimized hyperparameters. 5. Evaluation: Evaluation employing recursive multi-step-ahead forecasting without retraining, as frequent retraining is often not required to maintain comparable forecast accuracy while reducing computational costs [72], although distribution shifts may require model updates [11, 12]. Figure 4 illustrates this in more detail. Similar to fine-tuning Chronos-2, XGBoost and random forest are trained on the same training block using the hyperparameters listed in Table A.6 and the evaluation setup shown in Figure 4. For hyperparameter optimization, a subset of at most 5 000 time steps is drawn from the end of the training block; this subset is further split 80/20 into an hyperparameter optimization (HPO) training and an HPO validation set used as the Optuna objective. Final models are then retrained on the full training block, with lag features constructed from a context window of length C to ensure comparability with the TSFMs. All experiments were conducted on a multi-GPU server equipped with 2× AMD EPYC 9334 CPUs, 1.1 TiB of memory, and 4× NVIDIA RTX 6000 Ada Generation GPUs (48 GB VRAM each). Running the complete benchmark in parallel across multiple workers required approximately one week of wall-clock time, with the dominant share attributed to the training of random forest and XGBoost models as well as the fine-tuning of Chronos-2. The benchmark and in particular inference of the foundation models can also be executed on a single, less powerful GPU. 4.4. Evaluation Figure 4 illustrates the rolling evaluation scheme applied uniformly across all datasets and model types. Each dataset is split into a training/fine-tuning block of datasetdependent length and a fixed evaluation block, on which all models are evaluated under identical conditions. In the following, we first introduce the forecasting error metric and the Forecastability Index, then describe the benchmark configuration along three key dimensions, and finally detail the training and evaluation procedure. We evaluate the forecasting performance using the Normalized Root Mean Squared Error (NRMSE), a standard metric in energy forecasting that enables comparison across time series with different scales and units. Using the mean absolute value of the observations |y| defined as n

|y| =

1X |yi |, n i=1

where yi denotes the observed values and n the number of time steps, the NRMSE for the predicted values ŷi can be determined as v u n X 1 u t1 NRMSE = (yi − ŷi )2 . n i=1 |y| We normalize using the mean absolute value, since this is more robust for approximately stationary signals with near-zero means. Such time series are for instance occurring for battery storage dispatch profiles where charging and discharging power approximately

Dataset sample length N Full Dataset HPO Optimization

HPO Training

Training Finetuning

Val

Training Context H

Evaluation Shift 0

Evaluation block

start

Context H

Evaluation Shift 1

Evaluation block steps Context H

Evaluation Shift 2

Evaluation block .. .

.. .

Evaluation Shift K

Context H

Evaluation block start eval block t0

Evaluation block

Training Context

end eval block tend

train end

Full dataset

end

Validation

time

Horizon (H)

End buffer

Figure 4: Data splitting and rolling evaluation scheme. Each dataset is divided into a training/fine-tuning block of dataset-dependent length and a fixed evaluation block of 4,500 steps plus a 1,000-step buffer matching the maximum forecast horizon of Chronos-2. Within the evaluation block, a rolling scheme shifts the context window and horizon H in steps of 132, yielding W = ⌈4,500 / 132⌉ = 35 windows per model and horizon.

cancel out over operating cycles. Furthermore, this normalization allows for an approximate interpretation as a percentage error, making NRMSE particularly intuitive, with, e.g., a NRMSE of 0.05 corresponding approximately to 5% deviation from typical signal levels. To assess the model performance across our diverse collection of datasets, we further aim to quantify the intrinsic predictability of each time series independent of model choice. Analogous to Shannon’s 1951 finding [73] that English is predictable due to its low entropy (resulting from non-random letter frequencies), spectral entropy may quantify time series predictability by measuring deviation from uniform frequency distributions and therefore periodicity. Hence, we employ the spectral entropy-based Forecastability Index ϕ [74], a widely used metric for determining time series complexity, defined as ϕ=1−

where pk = |Fk |2 /

m X

H Hmax

with

H=−

m X

pk log(pk ),

k=1

|Fj |2 represents the normalized power at frequency k, Fk are

j=1

the real Fast Fourier Transform (FFT) coefficients of the mean-centered series, and Hmax = log(m) is the maximum spectral entropy for m frequency components. Values range from 0 (random, unforecastable) to 1 (highly periodic, easily forecastable). For a comprehensive assessment of prediction performance, our benchmark study is configured along three key dimensions: Ó Context Length Three context lengths are evaluated: 672, 2,000, and 8,000 steps. The minimum of 672 steps corresponds to one week at 15-minute resolution – the most prevalent resolution across the dataset collection. The maximum of 8,000 steps represents a trade-off between the upper context limits of TimesFM-2.5 (16,384 steps) and FlowState (≈16,000 steps at scale_factor = 0.25; no architectural sequencelength constraint) on the one hand, and the shorter context windows of Chronos-2 (8,192 steps) and TiRex (2,048 steps) on the other; Chronos-2 is evaluated near its maximum at this length. FlowState’s SSM-based encoder can in principle process arbitrarily long contexts, subject only to available memory; the pretrained checkpoint specifies a default context length of 4,096 steps. TabPFN-TS is not constrained by a fixed context window but operates on the underlying TabPFN-2.6 model, for which a recommended maximum of 50,000 samples applies; both are evaluated at the same lengths for comparability. The intermediate length of 2,000 steps was identified as a favorable trade-off in a preliminary sensitivity analysis and approximates the maximum context length of TiRex. Ó Forecast Horizon Horizons of 96, 192, and 288 steps are used, corresponding to 1, 2, and 3 days at 15-minute resolution. These intervals cover typical short-term forecasting periods relevant to operational energy systems planning. Ó Rolling Windows Evaluation is performed over 35 rolling windows with a step size of 132 steps. The number of windows reflects a trade-off between the length of the

shortest dataset and total computation time, while ensuring coverage of diverse temporal conditions including varying times of hour, day, weekdays, and months. Full seasonal cycles cannot be adequately represented due to the limited length of several datasets. The training and evaluation procedure visualized in Figure 4 is implemented as follows: For HPO-based models (XGBoost, random forest), a subset of the training block is split 80/20 into a training and a validation set for hyperparameter search; once the optimal hyperparameters are found, the model is retrained on the full training block. For finetuning-based models, the full training block is used directly without any validation split. To ensure comparability with TSFMs, lag features for random forest and XGBoost are constructed from a context window of length C, matching the TSFM context window.

5. Results We present our results in three parts: (1) an aggregated overview across all data categories and model configurations, (2) an analysis of the relationship between forecastability and prediction performance, and (3) a sensitivity analysis of the top-performing model investigating the influence of context length, forecast horizon, and aggregation level. Detailed per-dataset results are provided in the Appendix in Tables B.7, B.8, and B.9. 5.1. Results Overview Table 4 presents the aggregated results of all benchmark experiments. Figure 5 illustrates the underlying aggregation pipeline: experiment-level NRMSE values are first aggregated per (dataset, target) – as reported in Tables B.7, B.8 and B.9 – then per data category, and finally globally across all experiments to form the overall and best-count rows of Table 4. Mode Model

univariate / covariate / training

Dataset × Target

Context Length

54 series

{672, 2000, 8000}

Single Experiment one NRMSE value

Rolling Windows

Horizon {96, 192, 288}

≈ 35 shifts

≈ 17,010 experiments per mode

Min, Q25, median, Q75, Max

Aggregate over rolling windows, context length, horizon per model, per (dataset, target)

⇒ Tables B.7, B.8, B.9

median of medians, (Q10, Q90)

Aggregate over datasets within category

⇒ Table 4

per model, per data category

Overall Row

Best Count Row

median across all experiments

wins per (dataset, target, context, horizon)

Figure 5: Aggregation pipeline of the benchmark results, from individual experiments to the per-category, overall, and best-count rows of Table 4.

Each row reports the average of the median NRMSE values across all experiments within a given data category. The experiments cover different model modes and forecasting models as described in Section 4.3. The summary row overall reports the overall median NRMSE across all experiments. The best count row indicates the number of times a model achieves the best performance for a given experimental setting, defined by identical horizon length, context length, and prediction target, while varying rolling windows and covariate configurations. We observe that covariate-informed approaches achieve the best performance with the lowest overall median NRMSEs across these three approaches ranked first and dominate in

terms of total wins across all 17,010 experiments (Table 4). Chronos-2 (covariate) achieves both the overall lowest median NRMSE of 0.421 and the most wins among all individual model modes with 3,399 wins (20%). Figure 6 further illustrates the complementary strengths of the two best-performing (in terms of the median NRMSE) models through a closer pairwise comparison between Chronos-2 (covariate) and TabPFN-TS (covariate). Chronos-2 (covariate) achieves a higher overall win rate across all paired experiments and prevails in the majority of individual experiment settings within each data category. Table 4: Results overview across all benchmark modes. Each cell shows the averaged median NRMSE across all datasets and configurations for each data category and prediction model. Best median per benchmark highlighted. Best Count shows wins across all benchmarks. Total: 17,010 unique experiments (Dataset:Target × Rolling Windows × Horizon × Context Length) evaluated for each model across different benchmark modes. Values shown as median with (Q10, Q90) interval for classes and overall row. For Best Count, All = Total - Ties = 17,010 - 9 = 17,001. A orange background marks the best model within each benchmark mode, while a green background highlights the overall best across all modes in each row. Data Category

Univariate

Covariate

Training

TimesFM

Chronos-2

FlowState

TiRex

Chronos-2

TabPFN

TimesFM

Chronos-2

RandomForest

XGBoost

Balancing Services

2.24

2.26

2.25

2.27

2.26

2.24

2.57

2.25

2.50

2.61

⟨1.65, 6.28e5⟩

⟨1.63, 6.21e5⟩

⟨1.64, 1.99e6⟩

⟨1.65, 6.21e5⟩

⟨1.65, 2.00e6⟩

⟨1.64, 6.71e6⟩

⟨1.74, 2.15e8⟩

⟨1.63, 7.37e7⟩

⟨1.63, 1.68e10⟩

⟨1.63, 1.25e9⟩

Dispatchable Generation

0.410

0.384

0.451

0.459

0.398

0.428

0.654

0.707

0.639

0.535

⟨0.342, 0.519⟩

⟨0.359, 0.487⟩

⟨0.346, 1.02⟩

⟨0.398, 0.545⟩

⟨0.267, 0.456⟩

⟨0.295, 0.461⟩

⟨0.387, 0.695⟩

⟨0.524, 1.47⟩

⟨0.462, 1.19⟩

⟨0.385, 0.577⟩

Grid Data

0.567

0.544

0.530

0.590

0.437

0.427

0.450

0.498

0.597

0.489

⟨0.125, 0.921⟩

⟨0.118, 0.849⟩

⟨0.120, 0.905⟩

⟨0.121, 0.909⟩

⟨0.112, 0.510⟩

⟨0.116, 0.589⟩

⟨0.137, 0.656⟩

⟨0.154, 0.862⟩

⟨0.223, 0.891⟩

⟨0.173, 0.647⟩

0.827

0.796

0.816

0.849

0.778

0.822

0.815

0.793

0.997

0.990

⟨0.283, 0.894⟩

⟨0.282, 0.885⟩

⟨0.287, 0.918⟩

⟨0.292, 0.952⟩

⟨0.245, 0.898⟩

⟨0.272, 0.967⟩

⟨0.300, 0.946⟩

⟨0.269, 0.842⟩

⟨0.343, 1.17⟩

⟨0.305, 1.16⟩

0.031

0.032

0.092

0.037

0.029

0.064

0.066

0.146

0.098

0.062

⟨0.027, 0.196⟩

⟨0.028, 0.181⟩

⟨0.038, 0.189⟩

⟨0.035, 0.202⟩

⟨0.026, 0.182⟩

⟨0.042, 0.200⟩

⟨0.051, 0.252⟩

⟨0.105, 0.415⟩

⟨0.051, 0.216⟩

Heat Data Load Market Data Mobility Data Non-Dispatchable Generation Residential Load Overall Best Count (All)

⟨0.041, 0.195⟩

0.313

0.319

0.333

0.319

0.295

0.288

0.386

0.332

0.485

0.545

⟨0.270, 0.537⟩

⟨0.258, 0.539⟩

⟨0.291, 0.520⟩

⟨0.275, 0.545⟩

⟨0.264, 0.495⟩

⟨0.268, 0.492⟩

⟨0.356, 0.637⟩

⟨0.286, 0.526⟩

⟨0.361, 0.689⟩

⟨0.501, 0.848⟩

0.683

0.699

0.578

0.862

0.698

0.655

0.712

1.01

0.865

0.808

⟨0.413, 1.09⟩

⟨0.411, 1.08⟩

⟨0.334, 1.04⟩

⟨0.455, 1.13⟩

⟨0.417, 1.08⟩

⟨0.384, 1.10⟩

⟨0.438, 1.13⟩

⟨0.465, 1.58⟩

⟨0.509, 1.22⟩

⟨0.482, 1.19⟩

0.588

0.570

0.618

0.581

0.269

0.333

0.346

0.566

0.614

0.441

⟨0.410, 0.993⟩

⟨0.387, 0.988⟩

⟨0.470, 1.26⟩

⟨0.401, 0.932⟩

⟨0.197, 0.674⟩

⟨0.256, 0.660⟩

⟨0.205, 0.700⟩

⟨0.271, 1.33⟩

⟨0.374, 1.18⟩

⟨0.322, 0.816⟩

0.798

0.783

0.796

0.785

0.788

0.806

0.857

0.806

0.917

0.961

⟨0.581, 1.07⟩

⟨0.578, 1.06⟩

⟨0.579, 1.03⟩

⟨0.582, 1.07⟩

⟨0.580, 1.07⟩

⟨0.584, 1.10⟩

⟨0.613, 1.17⟩

⟨0.593, 1.09⟩

⟨0.630, 1.31⟩

⟨0.678, 1.59⟩

0.589

0.575

0.612

0.591

0.421

0.432

0.523

0.617

0.659

0.603

⟨0.261, 0.980⟩

⟨0.250, 0.977⟩

⟨0.269, 1.04⟩

⟨0.265, 1.00⟩

⟨0.198, 0.839⟩

⟨0.229, 0.864⟩

⟨0.266, 1.02⟩

⟨0.271, 1.06⟩

⟨0.343, 1.17⟩

⟨0.319, 1.10⟩

1,121 (7%)

1,175 (7%)

1,650 (10%)

888 (5%)

3,399 (20%)

2,134 (13%)

1,521 (9%)

2,665 (16%)

961 (6%)

1,487 (9%)

Mode Winner

Category Winner / Overall Winner

+6.2%

+0.9% +2.3% +2.2%

0 -2.3%

-5.7%

-7.4%

-2.6%

100 80

-23.5%

−40

941 669 2,277

1,444 10,484

−60

726

907

1,938

1,055

527

−80

534

668

1,527

835

418

60 40

Win rate [%]

Rel. NRMSE [%]

−20

6,526 1,188

761

276

−100

319

−120

-116.5%

s d n ta ad on ata ata ata oa ice tio Lo t Da erati l L ity D Serv rid D et D nera a a i n e k e r G H bil Ge dent ing Ma ble G Mo lanc ble Resi a a a h h B atc atc isp isp D D n-

TabPFN Chronos-2

20 0

all

er Ov

Figure 6: Pairwise relative NRMSE comparison between TabPFN (covariate) and Chronos-2 (covariate), the two top-ranked models by overall median NRMSE (cf. Table 4). Bars show (Chronos − 2 − T abP F N )/Chronos − 2 × 100%; positive values (amber) favour TabPFN, negative values (blue) favour Chronos-2. Lines (right axis) show per-category win rates with absolute counts in parentheses. Overall, Chronos-2 wins 62% of the 17,010 paired experiments, yielding a net relative improvement of 2.6%.

5.2. Results Analysis Since our results overview shows that Chronos-2 achieves the overall lowest median NRMSE and the highest total number of wins across all experiments, and given that its pairwise performance advantage over the second-ranked TabPFN-TS (covariate) is considerably larger than vice versa, we focus on Chronos-2 in its three forecasting modes for further analysis. In Figure 7, we analyze the correlation between the Forecastability Index ϕ (see Section 4.4) and the forecasting performance defined as 1 − N RM SE, aiming to compare the prediction performance with the intrinsic predictability of a time series. Values with an NRMSE larger than one are clipped to zero. For each dataset–target combination and model mode (varying rolling windows, context lengths, and forecast horizons), we computed the median across all results. The plot reveals a strong correlation between forecasting performance and forecastability (r = 0.673, p < 0.001). As expected, datasets with higher intrinsic stability such as aggregated country loads, aggregated load on grids, and aggregated heat demands are considerably better predictable for Chronos-2. In contrast, highly volatile time series, including single residential loads or balancing services, show substantially lower predictability. Given this relatively high correlation, the Forecastability Index ϕ may serve as an indicator for the predictability of a data category. However, it does not provide an absolute measure, meaning that the scaling of ϕ and the actual forecast score (1-NRMSE) may not be directly proportional, i.e., a high ϕ does not guarantee a correspondingly high forecast performance in absolute terms.

Forecastability vs. Forecast Performance (Chronos2, all settings)

Forecast Score (1-NRMSE)

Data Categories

0.75

Balancing Services Dispatchable Generation Grid Data Heat Data Load Market Data Mobility Data Non-Dispatchable Generation Residential Load

0.50

Mode

1.00

r = 0.673, p < 0.001

Univariate Training Covariate

0.25

0.00 0.0

0.2

0.4

0.6

0.8

1.0

Forecastability ϕ

Figure 7: Forecastability analysis for Chronos-2 across all experimental settings. The x-axis shows the Forecastability Index ϕ of each dataset – a measure of inherent predictability based on signal regularity – while the y-axis reports the forecast score (1-NRMSE), where higher values indicate better performance. A positive correlation (r = 0.673, p < 0.001) confirms that datasets with more regular patterns yield consistently better forecasts. Datasets with higher aggregation levels – such as grid data and heat data (upper right) – exhibit both high forecastability and strong forecast scores, suggesting that spatial or temporal aggregation smooths stochastic variability. In contrast, granular datasets such as individual residential load profiles cluster in the lower-left region. Surprisingly, some cases with high forecastability but near-zero forecast scores may indicate catastrophic forgetting during fine-tuning [75], which remains an open question for future work (see Section 6).

5.3. Sensitivity Analyses We further examine the influence of three key parameters on the performance of the overall best performing model Chronos-2 (covariate), i.e., the context length, the forecast horizon, and the data aggregation level. All experiments maintain the same configurations as the main benchmark settings (see the benchmark overview in section 4 and the evaluation scheme in section 4.4) to ensure consistency and comparability. First, we analyze the sensitivity with respect to the context length, increasing it from 100 to 8,000 time steps (the maximum context length of Chronos-2). In Figure 8, we show the results for four different datasets. The four datasets are representative examples drawn from three data categories – load data (country-level and industrial aggregation), market data, and grid data – with consistent behavior observed across additional datasets within each category; analogous plots for all datasets are provided in the supplementary material. Across all datasets and forecast horizons, we observe a relatively consistent pattern with a decreasing median NRMSE as context length increases, with performance saturating at a context length of approximately 2,000 time steps. We further examine the influence of the forecast horizon, gradually increasing it from 100 up to 1,000 time steps (the maximum horizon supported by Chronos-2). We again selected the same four datasets and show the results in Figure 9. Across all datasets and context lengths, the analysis reveals a decrease in predictive performance as the horizon length increases, reflecting the well-known effect that forecasts become increasingly uncertain the further they extend into the future. For a shorter context length, this performance decrease is a bit more pronounced and sets in earlier. For analyzing the effect of the aggregation level in Figure 10, we use the datasets HTW Berlin Households [55], Mobilithek [42], and Industrial VEA Profiles [53], selected from residential load, market data, and mobility data as representative datasets containing multiple target variables suitable for aggregation. Here, we observe that the forecast error consistently decreases with increasing aggregation level. This decrease indicates that temporal smoothing through aggregation improves overall forecasting accuracy. This behavior is characteristic for aggregated energy time series and aligns with the concept of standard load profiles, where larger aggregated groups of consumers tend to exhibit more predictable, standardized patterns [76, 77].

Horizon 96

0.20

0.15

0.10

0.05

0.00

0.00 10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.20

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.20

0.700

0.525

0.350

0.175

0.000

0.000 10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.700

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.700

0.250

0.125

0.000

Context Length

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.250

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.250

0.375

0.500

0 00

0.500

Context Length

Horizon 288

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.0

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

0.0 00

0.1

0.2

NRMSE NRMSE

0.4 0.3

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

NRMSE

Industrial VEA 2 Agg Profiles California Caiso

Horizon 192

0.3

10 0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 80 00

FR Power

0.4

0.3

0 00

NRMSE

Netze BW LV, Feeder 160

0.4

Context Length

Figure 8: Context length sensitivity analysis for Chronos-2 (covariate mode) across four representative datasets spanning load, market, and grid data categories, evaluated at forecast horizons of 96, 192, and 288 time steps. Each box plot summarizes the NRMSE distribution across all rolling windows within the respective dataset, with the red dashed line indicating the median trend. Context length ranges from 100 to 8,000 time steps (maximum supported by Chronos-2). Datasets include country-level (FR Power) [40] and industrial load aggregations (Industrial VEA) [53], market data (California Caiso) [51], and grid data (Netze BW LV) [60].

Context 672

Context 2000

0.3500

0.1750

0.0875

0.0000

0.09

0.06

0.03

0.00

0.00 0.60

0.45

0.30

0.15

0.00

0.00 4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.60

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.60

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.60

0.45

0.30

0.15

0.00

Horizon

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.60

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.60

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

NRMSE NRMSE

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.12

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.12

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.12

Horizon

Context 8000

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.2625

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

0.2625

NRMSE

DE Power Industrial VEA 2 Agg Profiles California Caiso

0.3500

0.2625

4 100 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 0 10 00

NRMSE

Netze BW LV, Feeder 160

0.3500

Horizon

Figure 9: Forecast horizon sensitivity analysis for Chronos-2 (covariate mode) across four representative datasets, evaluated at context lengths of 676, 2,000, and 8,000 time steps. The x-axis spans forecast horizons from 100 to 1,000 time steps, reflecting the full supported range of Chronos-2. Each box plot summarizes the NRMSE distribution across all time series within the respective dataset, with the red dashed line indicating the median trend. Datasets include country-level (DE Power) [40] and industrial load aggregations (Industrial VEA) [53], market data (California CASIO) [51], and grid data (Netze BW LV) [60].

0.22

0.15

0.07

0.00

0.75

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Figure 10: Aggregation level sensitivity analysis for Chronos-2 (covariate mode) across three representative datasets – residential household demand [55], EV charging stations [42], and industrial load profiles [53] – evaluated at forecast horizons of 96, 192, and 288 time steps. The x-axis represents the number of aggregated individual time series, ranging from a single profile up to the full available pool. Each box plot summarizes the NRMSE distribution, with the red dashed line indicating the median trend. The decreasing error with increasing aggregation level reflects the smoothing effect of temporal aggregation, characteristic of energy demand patterns described by standard load profiles [76, 77].

6. Discussion Figure 2 provides an overview of the wide variation and diverse stakeholder interests within energy-related forecasting. This illustration demonstrates the breadth of the domain and shows that general-purpose benchmarks such as GIFT-EVAL [15] and FEV-Benchmark [16] underrepresent energy-specific challenges by collapsing the domain into a single energy category. Our chosen categorization represents a deliberate trade-off between a datasetlevel view, which would be too fragmented, and such a monolithic energy data category, which obscures distinct stakeholder perspectives and forecasting requirements. Our dataset selection, though limited to available open data, aims to bridge this gap between generalpurpose benchmarks and the energy forecasting view. Future extensions could incorporate additional datasets to achieve broader geographic coverage, finer subdivisions within each data category. In particular, a finer-grained structure would allow to capture the heterogeneity within certain categories more accurately. Nonetheless, the fundamental insights presented here are unlikely to change substantially. 6.1. Model Performance Table 4 demonstrates that TSFMs in covariate and zero-shot settings consistently deliver superior performance across energy data categories. Notably, TSFMs outperform specialized models including XGBoost and random forest, even when these models are optimized taskspecifically using automated hyperparameter tuning and feature engineering. Additional manual feature engineering might further improve specialized model performance for specific datasets, but similar optimization opportunities exist for TSFMs through covariate engineering and fine-tuning. Overall, this zero-shot predictive superiority of covariateinformed TSFMs substantially reduces the need for dataset-specific model architectures and training procedures, enabling rapid deployment and scalability across the energy industry. Further advantages are that (1) no data-specific information can be incorporated in parameters during model training, often an issue for sensitive energy data and that (2) no computationally expensive model updates in the context of changing data distributions that often occur in time series are needed. 6.2. Forecastability and Aggregation Effects Figure 7 establishes the relationship between forecasting performance and the Forecastability Index ϕ, providing practitioners with a heuristic for assessing time series predictability prior to model deployment. Stationary time series exhibit higher ϕ values due to their regularity, correlating with superior forecast performance, while unstable signals show lower ϕ values and reduced predictability. Aggregated load categories – including country-level load data, grid data, and district heat data – consistently exhibit superior forecastability compared to individual residential loads or balancing service activations characterized by high temporal irregularity. The aggregation sensitivity analysis in Figure 10 confirms these findings, indicating an inverse relationship between aggregation level and forecasting error. From an energy systems forecasting perspective, these results suggest prioritizing grid-level or communitylevel coordination over individual asset optimization, as higher aggregation yields more reliable forecasts than single residential household or asset-level approaches. Since forecasts

serve as direct inputs to energy optimization workflows, more accurate forecasts typically translate into better optimization outcomes, e.g., in terms of cost savings or revenue. This supports the concept of local energy communities, where clusters of participants (prosumers, industrial and commercial consumers) are coordinated together rather than optimized in isolation, and aligns with established standard load profile concepts [76, 77], where larger consumer aggregations exhibit more predictable consumption patterns. 6.3. Limitations Despite recent advances in machine learning methods, inherent forecast uncertainty persists in energy time series. Certain data categories remain particularly difficult, such as balancing services with their complex and stochastic system dynamics or individual residential loads that are strongly shaped by individual household behavior, reflecting the irreducible uncertainty inherent to the stochastic nature of the system. A first limitation of this work is the reliance on publicly available datasets, which underrepresent several relevant asset types and stakeholder perspectives for which no open data is available, as well as some market designs and regulatory environments. Moreover, our evaluation remains restricted to independent data categories rather than coherent, system-wide compositions. As a result, our findings may not directly transfer to all regional contexts or highly specialized industrial applications, even though the qualitative patterns around aggregation and TSFM performance are likely to be robust. Expanding dataset coverage to include more countries and market structures would provide broader validation, though fundamental insights regarding aggregation benefits and TSFM superiority are unlikely to change with extended coverage. Second, our evaluation focuses on point forecasts and a single class of error metrics. We do not provide a full probabilistic assessment of uncertainty, nor do we study asymmetric cost structures or tail risks in depth. In operational settings, operators should therefore complement point forecast accuracy with scenario analysis or probabilistic methods that explicitly represent residual uncertainty. Finally, while we compare strong baselines and state-of-the-art TSFMs, we do not exhaust the design space of model architectures, fine-tuning strategies, or feature engineering pipelines. There may exist configurations that perform better on specific datasets than those reported here. Consequently, our results should be interpreted as evidence for the competitiveness and practicality of TSFMs in energy forecasting, rather than as a definitive upper bound on achievable performance. 6.4. Recommendations Based on these findings, we outline practical recommendations for practitioners and policymakers. Our results indicate that the most promising practical setup is to use state-ofthe-art TSFMs in the covariate mode for in-context learning with typical exogenous features such as weather variables and temporal features. In practice, this suggests that future deployments should focus on such covariate setups, where there is still substantial feature engineering potential by systematically experimenting with different feature combinations and transformations. Fine-tuning of large models in this domain is still an active research topic, and given the urgent need for acceleration of the energy transition, it seems advisable

to wait for more mature evidence and improved fine-tuning algorithms before relying on large-scale fine-tuning in production systems. From a policy perspective, it appears more beneficial to prioritize regulations that explicitly enable energy sharing, energy cells, and aggregation at higher grid levels, rather than predominantly focusing on optimizing individual assets in isolation. By shifting the regulatory focus towards coordinated operation and forecasting at aggregated levels, system operators can exploit the improved forecasting accuracy that modern models provide at these scales, which is likely to yield higher overall socio-economic value. From a broader perspective, these findings raise the question of whether regulatory frameworks should facilitate such coordination and aggregation rather than incentivize isolated single-asset optimization, a direction that the forecasting evidence presented here would support, but whose broader implications go beyond the scope of this work. 7. Conclusion This work demonstrates that time series foundation models are not only viable for diverse energy forecasting applications but frequently outperform specialized models such as XGBoost and random forest regressors, i.e., the current state-of-the-art, across multiple data categories. Critically, TSFMs eliminate the need for extensive model training, requiring only a context window rather than year-long historical datasets. This substantially reduces deployment time and directly addresses a central barrier of data-scarce applications in the energy domain – including newly commissioned renewable generation assets that lack sufficiently long historical records, operator portfolios constrained by organisational data silos arising from unbundling requirements and market regulation, as well as niche applications and small-scale energy assets for which the effort of training dedicated models is typically not justified – thereby unlocking significant scalability potential even in fragmented, data-limited deployment environments. Our analysis establishes spectral entropy as an effective forecastability indicator, enabling practitioners to assess predictability limits prior to deployment. Furthermore, aggregated datasets consistently show better predictability compared to individual time series, with forecast error decreasing with aggregation level. A natural next step would be to evaluate TSFMs on a holistic representation of a regional energy system – jointly covering individual households and industrial sites, lowand medium-voltage distribution grids, and transmission-level loads and generation within a single geographic region – to assess whether a shared forecasting backbone can consistently capture dependencies across aggregation levels instead of forecasting each level in isolation. Future work should also investigate fine-tuning strategies for TSFMs tailored to specific energy data categories or trained across all energy time series collectively, and explore how different foundation models can be combined, for example through simple ensembles or complementary in-context prompts. In addition, more systematic covariate engineering for TSFMs – including the design and evaluation of domain-specific feature sets for weather, markets, and operational constraints – remains an open engineering task. The demonstrated ability of TSFMs to generalize across diverse energy time series data categories without dataset-specific retraining suggests a promising direction for future work, i.e., investigating whether such universal forecasting properties can serve as a key

component in emerging dynamic network management schemes. This could be a first step towards fully dynamic flexible connection agreements, where asset-agnostic forecasting across heterogeneous grid-connected assets is a direct operational prerequisite, and in further steps towards fully dynamic grid tariffs that require consistent, portfolio-wide load and generation forecasting across all connected stakeholders, including an individual assessment of each network line. Given the rapid pace of development in this field, with continuously emerging novel TSFM models, ongoing evaluation remains essential; while this study builds on the most recent approaches available at the time, future work should continue to incorporate and assess newly developed models.

CRediT Author Statement Marco Obermeier: Conceptualization, Methodology, Software, Visualization, Formal Analysis, Data Curation, Investigation, Writing – Original Draft. Marco Pruckner: Supervision, Writing – Review & Editing. Florian Haselbeck: Supervision, Writing, Funding acquisition – Review & Editing. Andreas Zeiselmair: Supervision, Writing, Funding acquisition – Review & Editing. Declaration of Generative AI and AI-assisted Technologies During the preparation of this work, the authors used AI-assisted tools for language editing and code development. After using these tools, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication. Declaration of Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors thank the open-source community for providing the tools and libraries this work builds on, including Chronos, TimesFM, TiRex, FlowState, XGBoost, and random forest. We further thank all data providers for making their datasets publicly available, enabling reproducible research in the energy domain. The initial idea for this work emerged during the first author’s prior collaboration with the TiRex development team at Johannes Kepler University Linz (JKU), whose pioneering work on zero-shot time series forecasting provided the key inspiration for this research. The work was subsequently realized and further improved at Weihenstephan-Triesdorf University of Applied Sciences within the smartBattery project, funded by the Deutsche Bundesstiftung Umwelt (DBU) under grant number 40164-01 and co-funded by Bayernwerk Netz GmbH. The smartBattery project investigates AI-based methods for the grid-serving integration of large-scale battery storage systems. Within this context, the present work contributes universal and generalizable forecasting approaches – including envelope-based predictions – as a foundational step toward the implementation of dynamic grid tariffs.

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[74] Kang Y, Hyndman RJ, Smith-Miles K. Visualising Forecasting Algorithm Performance Using Time Series Instance Spaces. International Journal of Forecasting 2017; 33(2): 345–358. https://doi.org/10.1016/j.ijforecast.2016.09.004 [75] Karaouli N, Coquenet D, Fromont E, Mermillod M, Reyboz M. Are Time Series Foundation Models Susceptible to Catastrophic Forgetting? arXiv preprint 2025; arXiv:2510.00809. https://doi.org/10.48550/arXiv.2510.00809 [76] VDEW (Verband der Elektrizitätswirtschaft). Repräsentative VDEW-Lastprofile. VDEW Materialien, Frankfurt am Main; 1999. https://www.bdew.de/media/documents/ 1999_Repraesentative-VDEW-Lastprofile.pdf (Accessed: 23 November 2025). [77] BDEW (Bundesverband der Energie- und Wasserwirtschaft). Standardlastprofile Strom. Berlin; 2025. https://www.bdew.de/energie/standardlastprofile-strom/ (Accessed: 29 March 2026).

Appendix A. Data Statistics & Model Specifications

Table A.5: Dataset Statistics Overview: Comprehensive characteristics of all time series datasets including sample size (N), temporal resolution (Frequency), coefficient of variation (CV), percentage of negative and positive values, and forecastability index (ϕ). The forecastability index is based on spectral entropy, where values closer to 1 indicate more predictable time series with strong periodic patterns, while values near 0 suggest higher randomness and lower predictability. Dataset

Target

Frequency

Neg.%

Pos.%

Germany aFRR positiv Area Control Error (NRV Saldo) Germany aFRR negativ TenneT positiv TenneT negativ

348,576 364,303 348,576 383,704 383,704

15min 15min 15min 15min 15min

1.769 9.550 1.734 8.780 11.994

0.0% 45.5% 0.0% 0.0% 0.0%

90.2% 54.5% 92.0% 2.3% 1.4%

0.1428 0.1343 0.1286 0.1095 0.0961

Aggregated Batterys Fossil Hard Coal Fossil Gas

44,352 202,844 202,844

5min (100%), 1.1h (0%) 15min 15min

18.011 0.722 0.562

51.7% 0.0% 0.0%

48.2% 100.0% 100.0%

0.8084 0.6055 0.5916

Active Power Grid Consumption MS Grid Feed-in MS Active Power Active Power Active Power Active Power Active Power UW Wieselbach UW Lauchstädt L472 UW Wieselbach UW Lauchstädt L471 UW Lubmin - OWP Baltic Eagle

70,171 35,136 35,136 69,877 70,150 70,104 70,169 70,173 19,729 19,729 13,057

15min (100%), 45.0min (0%) 15min 15min 15min (100%), 2h (0%) 15min (100%), 1h (0%) 15min (100%), 1h (0%) 15min (100%), 2h (0%) 15min (100%), 1h (0%) 1h 1h 1h

0.343 0.274 0.564 1.642 26.891 4.826 0.482 2.007 0.620 0.652 0.995

0.0% 0.0% 0.0% 18.8% 27.4% 16.5% 0.0% 17.3% 0.0% 0.0% 0.0%

100.0% 100.0% 98.5% 81.2% 72.6% 83.5% 100.0% 82.7% 95.7% 93.4% 97.4%

0.7386 0.6738 0.6706 0.5776 0.5773 0.5263 0.5205 0.4949 0.3671 0.3473 0.2770

Heat Demand Heatpump 971151 Heatpump 818882

43,843 35,616 75,168

1h (100%), 2h (0%) 15min (100%), 1.0d (0%) 15min (100%), 1.0d (0%)

0.565 1.502 1.569

0.0% 0.0% 0.0%

100.0% 99.7% 100.0%

0.8657 0.3718 0.3160

Aggregated Load Load DE Load 2 random loads

44,352 202,844 71,259 35,136

5min (100%), 1.1h (0%) 15min 1h (62%), 15min (38%) 15min

0.189 0.177 0.218 0.560

0.0% 0.0% 0.0% 0.0%

100.0% 100.0% 100.0% 100.0%

0.7487 0.7406 0.6296 0.5909

LMP ZP26 LMP SP15 Day-Ahead Auction LMP NP15 Intraday Continuous reBAP

44,352 44,352 35,136 44,352 35,136 416,160

5min (100%), 1.1h (0%) 5min (100%), 1.1h (0%) 15min 5min (100%), 1.1h (0%) 15min 15min

0.474 0.556 0.810 0.410 1.028 2.827

4.8% 4.6% 5.2% 1.1% 6.7% 18.9%

95.1% 95.3% 94.1% 98.8% 93.3% 81.1%

0.5229 0.4032 0.3755 0.3623 0.2920 0.1215

Total Power Aggregated Profile 107 Total Power 50 Agg Total Power 50 Agg

143,922 17,376 228,179 35,058

15min 15min 15min 15min

2.354 0.387 1.423 1.585

0.0% 0.0% 0.0% 0.0%

44.9% 100.0% 66.7% 36.1%

0.6301 0.4608 0.3955 0.2278

Aggregated Solar Solar generation_kwh_UG Hall4 Solar Solar Solar_MWh_credit Wind Onshore Wind Offshore total_MWh_credit Wind_MWh_credit active_power

44,352 202,844 55,577 71,293 50,660 61,505 202,844 202,844 61,505 61,505 58,434

5min (100%), 1.1h (0%) 15min 15min 1h (62%), 15min (38%) 1h 30min (100%), 1h (0%) 15min 15min 30min (100%), 1h (0%) 30min (100%), 1h (0%) 15min (100%), 30min (0%)

1.295 1.537 1.624 1.439 1.759 1.631 0.802 0.686 0.667 0.761 1.166

48.4% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 17.2%

51.3% 72.6% 47.9% 60.5% 84.6% 52.0% 100.0% 99.9% 97.7% 94.3% 82.7%

0.8273 0.7628 0.6574 0.6342 0.6138 0.5749 0.4695 0.4189 0.3973 0.3672 0.3617

10 random aggregated households NO_PV_SFH31_P_TOT random_household_1 random_household_0 WITH_PV_SFH15_P_TOT NO_PV_SFH10_P_TOT random_household_2

35,040 88,425 35,040 35,040 69,210 89,630 35,040

15min 15min 15min 15min 15min 15min 15min

0.511 1.231 0.879 0.938 2.390 0.677 1.602

0.0% 0.0% 0.0% 0.0% 10.6% 0.0% 0.0%

100.0% 99.9% 100.0% 100.0% 89.4% 99.9% 100.0%

0.4222 0.2295 0.2256 0.2102 0.2020 0.1527 0.1339

Balancing services aFRR Germany Balancing Data Germany aFRR Germany mFRR Germany mFRR Germany Dispatchable Generation California Caiso ENTSO-E Germany ENTSO-E Germany Grid Data Netze BW LV, Feeder 37 Bayernwerk Bayernwerk Netze BW LV, Feeder 132 Netze BW LV, Feeder 97 Netze BW LV, Feeder 63 Netze BW LV, Feeder 160 Netze BW LV, Feeder 33 50Hertz Line Power 50Hertz Line Power 50Hertz Line Power Heat Data Heat Grid Flensburg HEAPO: Household Zurich Area HEAPO: Household Zurich Area Load California Caiso DE Power FR Power Industrial VEA 2 Agg Profiles Market Data California Caiso California Caiso ENTSO-E Germany California Caiso ENTSO-E Germany ENTSO-E Germany Mobility Data NL Office EV Park UrbanEV China Charging Station Mobilitaet Public Charging Station UK Residential Charging Station Non-Dispatchable Generation California Caiso DE Power PV Hong Kong FR Power DK Power Energy Forecasting Competition PV Cluster DE Power DE Power Energy Forecasting Competition Wind+PV Energy Forecasting Competition Windpark Hill of Towie Wind Residential Load HTW Berlin Households Household Lower Saxony HTW Berlin Households HTW Berlin Households Household Lower Saxony Household Lower Saxony HTW Berlin Households

Table A.6: Model Specifications. Hyperparameter search spaces and configuration for trained models. For XGBoost and Random Forest, Optuna TPE sampler is used with n = 250 trials. SHAP-based feature selection and automatic lag selection are enabled for both tree-based models.

Parameter

Chronos-2

XGBoost

Random Forest

– [0.1, 0.5, 0.9]

250 [0.1, 0.5, 0.9]

– – –

✓ 100 20

– – – –

[3, 6, 12, 24, 48, 96] mean, std, min, max ✓ 50

[100, 1000] (int) [3, 10] (int) [0.01, 0.2] (log) [0.3, 1.0] [0.2, 1.0] – – – –

[100, 1000] (int) [3, 30] (int) – – – [2, 20] (int) [1, 10] (int) {sqrt, log2, 0.5, 0.7, 1.0} {true, false}

– – – – – – – – –

General HPO Trials Quantiles Lag Selection Auto Lag Selection Max Lags to Test Top-k Lags Selected Feature Engineering Rolling Windows Rolling Features SHAP Feature Selection SHAP Top-k Features

Hyperparameter Search Space n_estimators max_depth learning_rate subsample colsample_bytree min_samples_split min_samples_leaf max_features bootstrap

– – – – – – – – –

Fine-Tuning (Chronos-2 only) Num Steps Learning Rate Batch Size Window Overlap LoRA Rank LoRA Alpha LoRA Dropout LoRA Target Modules Checkpoint

10 000 5 × 10−4 32 75% 1 1 0.15 {q} chronos-2

Appendix B. Extended Results This section extends the benchmark results: Figure B.11 shows an example prediction for one specific experimental setting, representative of the many configurations evaluated as described above. Tables B.7, B.8 and B.9 report the extended per-dataset results, which are summarized in Table 4. Historical Data Actual Values

Model Forecast Baseline Forecast

Uncertainty (10%-90%)

Forecast Start 2.6

Load [GW]

1.3

0.7

Covariates (normalized)

Context

Horizon

Shortwave Radiation Mean

Direct Radiation Mean

1 0.5 0

Time [days]

Figure B.11: Forecast evaluation for Bayernwerk MV Grid feed-in [59]: Historical data (blue), seasonal naive baseline forecast (orange), model forecast (red dashed), 10%-90% uncertainty interval (red shaded), and actual values (green). Model: Chronos-2 (covariate) | MASE: 0.4259 | CRPS: 0.2119 | NRMSE: 0.0677 | CORR: 0.9733 | SUM_RATIO: 1.0126

0.0000

All

Overall

Summary (Best Med)

0.2054 0.3236 0.2586 0.2762 0.1468 0.3307 0.3445

0.0161 0.1075 0.1438 0.0506 0.2945 0.1006 0.0317 0.1583 0.0545

0.5654 0.1317 0.9490 0.0590

0.0457 0.0434 0.0401 0.0514 0.0783 0.3008

0.0046 0.0075 0.0600

0.6061 0.5774 0.0682

0.5802 0.2538 0.2602 0.0122 0.0221 0.1300 0.1216 0.1943 0.0910 0.2152 0.1946

0.0370 0.0681 0.0758

1.1102 1.5004 1.6232 0.0000 0.0000

Min

10 random aggregated households random_household_0 random_household_1 random_household_2 NO_PV_SFH10_P_TOT NO_PV_SFH31_P_TOT WITH_PV_SFH15_P_TOT

Aggregated Solar Wind Offshore Wind Onshore Solar Solar_MWh_credit total_MWh_credit Wind_MWh_credit active_power generation_kwh_UG Hall4

Total Power 50 Agg Total Power Total Power 50 Agg Aggregated Profile 107

LMP NP15 LMP SP15 LMP ZP26 Day-Ahead Auction Intraday Continuous reBAP

Aggregated Load Load 2 random loads

Heatpump 818882 Heatpump 971151 Heat Demand

UW Lubmin - OWP Baltic Eagle UW Wieselbach UW Lauchstädt L471 UW Wieselbach UW Lauchstädt L472 Grid Consumption MS Grid Feed-in MS Active Power Active Power Active Power Active Power Active Power Active Power

Aggregated Batterys Fossil Gas Fossil Hard Coal

Area Control Error (NRV Saldo) Germany aFRR negativ Germany aFRR positiv TenneT negativ TenneT positiv

Target

HTW Berlin Households HTW Berlin Households HTW Berlin Households HTW Berlin Households Household Lower Saxony Household Lower Saxony Household Lower Saxony

Residential Load

California Caiso DE Power DE Power DK Power Energy Forecasting Competition PV Cluster Energy Forecasting Competition Wind+PV Energy Forecasting Competition Windpark Hill of Towie Wind PV Hong Kong

Non-Dispatchable Generation

Mobilitaet Public Charging Station NL Office EV Park UK Residential Charging Station UrbanEV China Charging Station

Mobility Data

California Caiso California Caiso California Caiso ENTSO-E Germany ENTSO-E Germany ENTSO-E Germany

Market Data

California Caiso FR Power Industrial VEA 2 Agg Profiles

Load

HEAPO: Household Zurich Area HEAPO: Household Zurich Area Heat Grid Flensburg

Heat Data

50Hertz Line Power 50Hertz Line Power 50Hertz Line Power Bayernwerk Bayernwerk Netze BW LV, Feeder 132 Netze BW LV, Feeder 160 Netze BW LV, Feeder 33 Netze BW LV, Feeder 37 Netze BW LV, Feeder 63 Netze BW LV, Feeder 97

Grid Data

California Caiso ENTSO-E Germany ENTSO-E Germany

Dispatchable Generation

Balancing Data Germany aFRR Germany aFRR Germany mFRR Germany mFRR Germany

Balancing Services

Dataset

0.2609

0.3102 0.7465 0.6193 1.1444 0.6390 0.7541 0.5665

0.1162 0.4405 0.4033 0.2810 0.6543 0.3403 0.4138 0.8881 0.4527

0.6784 0.3461 1.1148 0.2363

0.1604 0.1667 0.1418 0.2251 0.2135 0.5410

0.0171 0.0190 0.1575

0.8169 0.7656 0.1198

0.9613 0.5332 0.5038 0.0377 0.1065 0.3315 0.1762 0.4366 0.1124 0.6085 0.5068

0.2285 0.2366 0.3403

1.2367 1.9190 2.0210 9.9275 9.6732

Q25

0.5893

0.3513 0.8370 0.7681 1.3852 0.7346 0.8631 0.7981

0.3005 0.6191 0.5281 0.4378 0.9547 0.4641 0.5880 1.1473 0.7291

0.7732 0.5930 1.2195 0.3355

0.2879 0.2889 0.2526 0.3472 0.3366 0.7263

0.0307 0.0261 0.2376

0.9101 0.8273 0.1468

1.1269 0.6545 0.6460 0.0577 0.1519 0.4864 0.1947 0.5671 0.1253 0.9207 0.7182

0.4098 0.3256 0.5463

1.2720 2.2437 2.2147 >1 × 106 16.9706

Med

Q75

0.9799

0.4194 0.9183 0.8798 1.6087 0.8177 0.9787 1.0181

0.6896 0.8377 0.7156 0.5857 1.4541 0.6485 0.8019 1.5984 1.0829

0.8859 1.6968 1.3409 0.3973

0.4324 0.4820 0.3787 0.6108 0.6553 1.0369

0.0652 0.0385 0.3660

1.0925 0.8797 0.2087

1.3174 0.8129 0.8213 0.0875 0.2044 0.6434 0.2247 0.8047 0.1365 1.1432 0.9688

0.8917 0.4705 0.8292

1.3029 2.5947 2.3711 >1 × 106 >1 × 106

TimesFM

0.2144 0.3208 0.2757 0.2629 0.1513 0.3016 0.3217 0.0037

>1 × 106

0.0166 0.0860 0.0959 0.0420 0.2967 0.0649 0.0200 0.2446 0.0316

0.5436 0.1261 0.9283 0.0570

0.0435 0.0394 0.0369 0.0525 0.0669 0.2901

0.0037 0.0070 0.0397

0.3972 0.4960 0.0608

0.6880 0.2522 0.2549 0.0145 0.0298 0.1099 0.1216 0.1741 0.0893 0.1763 0.1675

0.0725 0.0680 0.0584

1.1452 1.4674 1.5813 5.0241 3.3430

Min

0.6060 1.4139 1.1060 2.0290 1.1985 1.2615 1.9725

10.7367 9.4488 2.8656 2.9561 4.0228 1.6414 5.5621 17.2201 9.4185

1.1034 >1 × 106 2.4936 0.9378

2.8132 2.8098 2.6519 7.9391 6.6634 3.7046

0.1746 0.2153 1.1253

1.9188 1.2598 0.5123

6.6974 2.1792 >1 × 106 0.2864 0.4697 1.2505 0.3479 1.5728 0.1982 2.2688 2.0410

5.1636 2.5190 3.0735

1.5922 3.9192 3.0295 >1 × 106 >1 × 106

Max

0.2496

0.3094 0.7438 0.6082 1.1363 0.6463 0.7151 0.5644

0.0853 0.4434 0.3964 0.2653 0.6316 0.3347 0.3962 0.9286 0.3231

0.6817 0.3489 1.1075 0.2261

0.1474 0.1685 0.1378 0.2277 0.2211 0.5432

0.0173 0.0191 0.1409

0.8005 0.7342 0.1205

0.9931 0.5443 0.5123 0.0358 0.1072 0.3014 0.1687 0.4015 0.1092 0.5238 0.3939

0.2318 0.2417 0.3127

1.2379 1.9179 2.0153 9.9727 9.7985

Q25

0.5754

0.3432 0.8249 0.7568 1.3790 0.7344 0.8554 0.7827

0.2142 0.6564 0.5072 0.4306 0.9131 0.4604 0.5701 1.2873 0.6935

0.7613 0.6374 1.2151 0.3145

0.2761 0.2951 0.2393 0.3718 0.3420 0.7057

0.0324 0.0274 0.2179

0.9079 0.7958 0.1535

1.1552 0.6624 0.6257 0.0617 0.1605 0.4558 0.1897 0.5440 0.1178 0.8486 0.6460

0.3840 0.3524 0.5126

1.2665 2.2559 2.1776 >1 × 106 17.0547

Med

Q75

0.9770

0.3943 0.8992 0.8704 1.5857 0.8222 0.9844 1.0048

0.6824 0.8930 0.7119 0.5846 1.4562 0.6492 0.8238 1.5871 1.1679

0.8860 1.6653 1.3291 0.3801

0.4015 0.4806 0.3652 0.6143 0.7047 1.0661

0.0653 0.0440 0.3061

1.0721 0.8734 0.2077

1.3330 0.8029 0.8164 0.1135 0.2264 0.6016 0.2106 0.7311 0.1287 1.1577 0.8761

0.7890 0.4816 0.8153

1.2977 2.5909 2.3586 >1 × 106 >1 × 106

Chronos-2

>1 × 106

0.5817 1.4158 1.1241 2.0357 0.9829 1.3166 1.4651

9.6076 4.1004 1.8734 2.4240 15.2554 1.6452 5.2720 8.1392 9.5096

1.0959 >1 × 106 2.9098 0.8690

1.7042 2.3125 1.8290 5.4755 4.2370 3.2393

0.1390 0.2547 0.9225

2.0255 1.4189 0.4943

5.7702 1.9118 >1 × 106 0.2605 0.5650 1.2908 0.3483 1.9702 0.1903 2.8368 2.6173

5.2918 1.3009 3.3689

1.6553 3.9434 2.9942 >1 × 106 >1 × 106

Max

0.0085

0.2136 0.3354 0.2479 0.2964 0.1559 0.3132 0.3393

0.2160 0.0437 0.0617 0.0480 0.3601 0.0846 0.0219 0.3924 0.0332

0.5308 0.1039 0.8428 0.0705

0.0381 0.0509 0.0421 0.0450 0.0725 0.3018

0.0131 0.0085 0.0547

0.5454 0.5142 0.0770

0.5589 0.2759 0.2642 0.0142 0.0198 0.1064 0.1293 0.2068 0.0885 0.2193 0.1902

0.2523 0.0486 0.0812

1.1002 1.3761 1.5732 5.0237 3.3416

Min

0.2693

0.2960 0.7274 0.6025 1.0959 0.6485 0.7083 0.5764

1.1188 0.4282 0.3900 0.2583 0.6117 0.3557 0.3954 0.9053 0.3284

0.6766 0.2840 1.0536 0.2333

0.1778 0.2065 0.1731 0.2001 0.2010 0.5271

0.0640 0.0182 0.1454

0.8250 0.7589 0.1271

0.9829 0.5520 0.5415 0.0334 0.1020 0.3327 0.1695 0.3989 0.1095 0.6545 0.4912

1.0166 0.2258 0.3276

1.2408 1.9080 1.9847 9.9760 9.7980

Q25

0.6124

0.3355 0.8097 0.7450 1.3382 0.7406 0.8277 0.7964

1.5730 0.6182 0.5614 0.4493 0.9638 0.4751 0.5927 1.1877 0.6297

0.7593 0.3965 1.1602 0.3078

0.3319 0.3094 0.2735 0.3336 0.3448 0.6962

0.0916 0.0246 0.2131

0.9436 0.8156 0.1547

1.1274 0.6824 0.6773 0.0551 0.1480 0.4460 0.1887 0.5298 0.1195 0.9052 0.6556

1.1642 0.3203 0.4507

1.2802 2.2475 2.1786 >1 × 106 31 076.3775

Med

FlowState

1.0372

0.3760 0.8918 0.8498 1.5532 0.8217 0.9529 1.0292

1.7675 0.8066 0.7443 0.6141 1.5438 0.6477 0.8137 1.5354 1.1071

0.8828 0.7210 1.2908 0.3923

0.5009 0.5612 0.4748 0.5938 0.6775 1.0369

0.1114 0.0339 0.3310

1.1038 0.8982 0.2228

1.3398 0.8327 0.8457 0.0798 0.2029 0.6841 0.2114 0.6799 0.1330 1.1607 0.9241

1.3004 0.4455 0.6805

1.3221 2.6100 2.3292 >1 × 106 >1 × 106

Q75

>1 × 106

0.5712 1.3971 1.1222 2.0444 0.9799 1.3098 1.4454

48.7086 4.2213 2.1291 3.3211 5.6379 1.8692 6.4125 7.0019 9.4934

1.0892 >1 × 106 3.1986 0.9540

3.1510 3.0968 3.0873 4.3833 4.1995 4.6700

0.2245 0.1628 0.7569

1.9389 1.6680 0.5272

7.6498 1.9322 >1 × 106 0.1807 0.4646 1.2517 0.3118 1.3660 0.1958 3.0774 2.7005

4.1418 2.1359 3.2897

1.9195 3.9422 3.0791 >1 × 106 >1 × 106

Max

0.0063

0.2020 0.3177 0.2774 0.2655 0.1516 0.3205 0.3347

0.0327 0.1554 0.0825 0.0649 0.3420 0.0703 0.0173 0.1660 0.0535

0.5595 0.1468 0.9233 0.0635

0.0604 0.0429 0.0507 0.0772 0.0924 0.2835

0.0063 0.0087 0.0723

0.4709 0.5597 0.0617

0.6119 0.2857 0.2608 0.0154 0.0433 0.1526 0.1245 0.2068 0.0911 0.2307 0.1863

0.0578 0.0746 0.0903

1.1047 1.5063 1.6454 5.0243 3.3414

Min

0.2646

0.3060 0.7403 0.6235 1.1505 0.6471 0.7524 0.5609

0.1038 0.4420 0.4021 0.2868 0.6122 0.3218 0.3872 0.9571 0.3935

0.6843 0.4851 1.1131 0.2352

0.1743 0.1702 0.1500 0.2393 0.2080 0.5182

0.0208 0.0247 0.1668

0.8367 0.7867 0.1225

0.9495 0.5245 0.5116 0.0459 0.1213 0.3340 0.1758 0.4325 0.1102 0.6025 0.4953

0.2680 0.2601 0.3023

1.2351 1.9684 2.0255 9.9718 9.7974

Q25

0.5905

0.3441 0.8317 0.7695 1.3804 0.7408 0.8589 0.7847

0.2193 0.6638 0.5275 0.4499 0.8650 0.4461 0.5814 1.1982 0.7196

0.7721 0.9513 1.2077 0.3192

0.2936 0.3029 0.2563 0.3706 0.3346 0.7193

0.0350 0.0365 0.2431

0.9771 0.8495 0.1529

1.1292 0.6407 0.6277 0.0717 0.1854 0.4573 0.2023 0.5895 0.1215 0.9090 0.6647

0.4593 0.3825 0.5658

1.2684 2.2692 2.2273 >1 × 106 85.6549

Med

TiRex

1.0019

0.3918 0.8967 0.8742 1.6014 0.8195 1.0032 1.0217

0.5696 0.8779 0.7230 0.5881 1.4393 0.6478 0.8395 1.5971 1.1508

0.8838 1.9453 1.3427 0.3778

0.4524 0.4973 0.3941 0.6125 0.7065 1.0016

0.0681 0.0548 0.3610

1.1372 0.9434 0.2146

1.3062 0.7847 0.7884 0.1148 0.2404 0.6265 0.2293 0.8681 0.1349 1.1201 0.9285

0.9531 0.5111 0.8641

1.3054 2.6453 2.3765 >1 × 106 >1 × 106

Q75

>1 × 106

0.6088 1.4037 1.1206 2.0325 0.9799 1.3367 1.4385

12.8219 5.4859 1.8420 2.5152 3.9177 1.6997 5.1944 9.8058 9.0453

1.0824 >1 × 106 2.4881 0.9186

2.2280 2.5378 2.1347 2.8122 4.3876 4.1459

0.1935 0.2142 1.0022

2.0890 1.4010 0.4705

4.4055 1.6158 >1 × 106 0.2408 0.5969 1.1951 0.3042 1.9930 0.1899 2.4372 2.2710

3.2916 1.1806 3.6839

1.7118 3.9375 3.0233 >1 × 106 >1 × 106

Max

Table B.7: Results Univariate Benchmark: Statistics (Min, Q25, Median, Q75, Max) over multiple forecast horizons and context lengths; best median per row highlighted. Overall row aggregates globally across all datasets, targets, horizons, and context lengths. Values > 106 are treated as diverged, unusable forecasts and displayed as > 106 .

All

Overall

Summary (Best Med)

10 random aggregated households random_household_0 random_household_1 random_household_2 NO_PV_SFH10_P_TOT NO_PV_SFH31_P_TOT WITH_PV_SFH15_P_TOT

Aggregated Solar Solar Wind Offshore Wind Onshore Solar Solar_MWh_credit total_MWh_credit Wind_MWh_credit Solar active_power generation_kwh_UG Hall4

Total Power 50 Agg Total Power Total Power 50 Agg Aggregated Profile 107

LMP NP15 LMP SP15 LMP ZP26 Day-Ahead Auction Intraday Continuous reBAP

Aggregated Load Load DE Load 2 random loads

Heatpump 818882 Heatpump 971151 Heat Demand

Aggregated Batterys Fossil Gas Fossil Hard Coal

Area Control Error (NRV Saldo) Germany aFRR negativ Germany aFRR positiv TenneT negativ TenneT positiv

Target

HTW Berlin Households HTW Berlin Households HTW Berlin Households HTW Berlin Households Household Lower Saxony Household Lower Saxony Household Lower Saxony

Residential Load

California Caiso DE Power DE Power DE Power DK Power Energy Forecasting Competition PV Cluster Energy Forecasting Competition Wind+PV Energy Forecasting Competition Windpark FR Power Hill of Towie Wind PV Hong Kong

Non-Dispatchable Generation

Mobilitaet Public Charging Station NL Office EV Park UK Residential Charging Station UrbanEV China Charging Station

Mobility Data

California Caiso California Caiso California Caiso ENTSO-E Germany ENTSO-E Germany ENTSO-E Germany

Market Data

California Caiso DE Power FR Power Industrial VEA 2 Agg Profiles

Load

HEAPO: Household Zurich Area HEAPO: Household Zurich Area Heat Grid Flensburg

Heat Data

Grid Data

California Caiso ENTSO-E Germany ENTSO-E Germany

Dispatchable Generation

Balancing Data Germany aFRR Germany aFRR Germany mFRR Germany mFRR Germany

Balancing Services

Dataset

All

Cal DE Cal DE Cal DE Cal DE Cal DE Cal DE Cal DE

Weather NP15, SP15, ZP26 PV scaled Weather Wind scaled Weather Wind scaled Weather DK Weather UK Weather Competition UK Weather Competition UK Weather Competition FR Weather Hill of Towie Weather Weather HK

DE Cal NL Cal UK Cal CN Cal

Weather NP15, Cal California Weather SP15, Cal California Weather ZP26, Cal California DE Weather + Calendar DE Weather + Calendar DE Weather + DE Cal

Weather NP15, SP15, ZP26, Cal California DE Weather + Calendar FR Weather DE Calendar

Zurich Weather + CH Cal Zurich Weather + CH Cal Weather + DE Cal

DE Weather + DE Cal DE Weather + DE Cal DE Weather + DE Cal DE Weather + Bayern Cal Bayern Weather + Bayern Cal Weather + BW Cal Weather + BW Cal Weather + BW Cal Weather + BW Cal Weather + BW Cal Weather + BW Cal

Weather NP15, SP15, ZP26, Cal California Wind + DE Weather + Cal Wind Weather + Calendar

DE Weather + Calendar DE Weather + Calendar DE Weather + Calendar DE Weather + Calendar DE Weather + Calendar

Covariates

0.0035

0.2118 0.3208 0.2753 0.2567 0.1522 0.2790 0.3080

0.0174 0.0284 0.0992 0.0492 0.2110 0.2330 0.0490 0.0168 0.0327 0.3068 0.0305

0.5398 0.1197 0.9279 0.0574

0.0416 0.0327 0.0411 0.0505 0.0665 0.2855

0.0035 0.0061 0.0072 0.0424

0.4433 0.4835 0.0629

0.3302 0.1848 0.1822 0.0113 0.0193 0.1143 0.1226 0.1784 0.0863 0.1628 0.1577

0.0789 0.0692 0.0606

1.1098 1.3804 1.5208 5.0220 3.3236

Min

0.1979

0.3170 0.7413 0.6186 1.1526 0.6449 0.7219 0.5587

0.0990 0.1035 0.2770 0.1366 0.3068 0.4612 0.1942 0.2196 0.1510 0.6157 0.1359

0.6739 0.3538 1.1149 0.2346

0.1594 0.1748 0.1391 0.1670 0.1988 0.4842

0.0156 0.0183 0.0181 0.1737

0.8110 0.7200 0.0965

0.5073 0.3841 0.3815 0.0354 0.0724 0.2264 0.1734 0.3801 0.1113 0.3864 0.3259

0.2549 0.1691 0.2965

1.2179 1.8931 2.0237 9.9662 9.7887

Q25

0.4212

0.3471 0.8305 0.7705 1.3937 0.7351 0.8577 0.7880

0.2338 0.1321 0.4284 0.1969 0.3595 0.6743 0.2693 0.2779 0.2034 0.8685 0.1976

0.7592 0.6365 1.2195 0.3225

0.2832 0.2931 0.2457 0.3076 0.2969 0.6818

0.0305 0.0245 0.0282 0.2465

0.9274 0.7784 0.1115

0.6144 0.4736 0.4555 0.0501 0.1122 0.2831 0.1911 0.4739 0.1216 0.5104 0.4365

0.3983 0.2341 0.4705

1.2641 2.2568 2.2174 >1 × 106 78.1965

Med

Q75

0.8390

0.4055 0.9067 0.8793 1.6018 0.8238 1.0074 1.0084

0.4379 0.1843 0.6102 0.2580 0.4751 0.9504 0.3840 0.4485 0.2584 1.1990 0.2738

0.8796 1.8206 1.3216 0.3987

0.4116 0.4813 0.3823 0.5176 0.5639 0.9786

0.0578 0.0355 0.0415 0.3913

1.0783 0.8235 0.1324

0.7413 0.6003 0.5696 0.0877 0.1568 0.3566 0.2201 0.6706 0.1381 0.6944 0.5757

0.7060 0.3183 0.7310

1.3029 2.6075 2.3556 >1 × 106 >1 × 106

Chronos-2

0.2264 0.3203 0.2859 0.2620 0.1632 0.4089 0.3170 0.0000

>1 × 106

0.1136 0.1384 0.1116 0.0509 0.1936 0.2544 0.0452 0.0122 0.1224 0.2516 0.0578

0.5411 0.1177 0.9341 0.0669

0.0445 0.0405 0.0405 0.0531 0.0812 0.3065

0.0085 0.0095 0.0294 0.0587

0.6089 0.4259 0.0527

0.1988 0.1736 0.1557 0.0123 0.0296 0.1121 0.1189 0.1878 0.0940 0.1915 0.1748

0.1091 0.0702 0.0884

1.1379 1.3242 1.4692 0.0000 0.0000

Min

0.6301 1.4163 1.1368 2.0393 0.9838 1.3404 1.4574

18.6959 0.5220 4.6673 0.8178 1.6605 5.7510 1.0916 2.0507 0.4520 5.4437 3.5576

1.0975 >1 × 106 2.7509 0.9393

1.9699 2.7238 4.6056 8.2622 4.1438 3.2507

0.1963 0.1773 0.1428 1.3553

2.0027 1.4320 0.4317

3.3675 1.6340 >1 × 106 0.2632 0.3775 1.2024 0.3471 1.8187 0.3119 1.2427 1.2360

4.2281 0.8428 3.3620

1.9846 3.9204 3.0173 >1 × 106 >1 × 106

Max

0.2292

0.3175 0.7567 0.6309 1.1797 0.6453 0.7657 0.5723

0.2621 0.2346 0.3043 0.1728 0.3032 0.4565 0.1999 0.2310 0.2187 0.7393 0.1816

0.6856 0.3519 1.1374 0.2522

0.1745 0.1746 0.1623 0.1585 0.2037 0.4980

0.0334 0.0268 0.0584 0.1790

0.8396 0.7545 0.1101

0.4781 0.3582 0.3392 0.0440 0.0880 0.2502 0.1799 0.3835 0.1127 0.4351 0.3578

0.3034 0.2008 0.2897

1.2311 1.9183 2.0053 10.0158 9.7845

Q25

0.4321

0.3498 0.8520 0.7714 1.4024 0.7410 0.9043 0.8065

0.3809 0.2856 0.4423 0.2146 0.3514 0.6598 0.2799 0.3325 0.2559 0.8834 0.2647

0.7770 0.5326 1.2423 0.3208

0.3230 0.3023 0.2655 0.2698 0.2746 0.6616

0.0528 0.0373 0.0742 0.2536

1.0034 0.8225 0.1338

0.5887 0.4557 0.4266 0.0674 0.1163 0.3311 0.2084 0.4721 0.1259 0.6159 0.4808

0.4689 0.2616 0.4278

1.2579 2.2365 2.2074 >1 × 106 17.5545

Med

TabPFN

0.8644

0.4038 0.9321 0.8860 1.6316 0.8258 1.0480 1.0373

0.9197 0.3740 0.5820 0.2627 0.4050 0.9509 0.3677 0.4773 0.3021 1.2185 0.3395

0.9019 0.9336 1.3663 0.3833

0.5090 0.5134 0.4469 0.4549 0.5450 0.9779

0.0780 0.0604 0.0948 0.3468

1.1804 0.8921 0.1723

0.7621 0.5872 0.5508 0.0997 0.1689 0.4262 0.2340 0.6485 0.1388 0.7839 0.6302

0.8494 0.3402 0.6374

1.2956 2.5840 2.3478 >1 × 106 >1 × 106

Q75

>1 × 106

0.5969 1.4116 1.1350 2.0394 0.9974 1.3889 1.4635

38.2988 0.8041 9.1248 0.5602 0.7409 5.2923 1.3726 2.0645 0.6066 11.2605 0.9689

1.0944 >1 × 106 2.5417 0.8975

3.4605 3.2643 3.2078 6.0116 3.9922 6.1900

0.1960 0.1916 0.1718 1.0180

2.2095 1.4935 0.4897

3.6510 1.7189 >1 × 106 0.2780 0.4761 1.0457 0.3475 1.4162 0.1980 1.3098 1.2514

3.9088 1.0426 3.6606

1.7726 3.8796 2.9707 >1 × 106 >1 × 106

Max

0.0000

0.2295 0.3129 0.2955 0.3147 0.1517 0.3271 0.3368

0.0892 0.0450 0.1312 0.0712 0.2200 0.1597 0.1022 0.1083 0.0760 0.2655 0.0657

0.5774 0.1271 0.9457 0.0595

0.0544 0.0466 0.0534 0.0508 0.1010 0.2706

0.0055 0.0149 0.0151 0.0737

0.6044 0.5281 0.0650

0.4069 0.2000 0.1444 0.0181 0.0265 0.1130 0.1287 0.1955 0.0945 0.2861 0.2347

0.1170 0.1081 0.1078

0.9381 1.3694 1.3803 0.0000 0.0000

Min

0.2660

0.3269 0.7692 0.6913 1.2217 0.6664 0.7491 0.6552

0.4256 0.1386 0.2967 0.1601 0.3263 0.4574 0.2282 0.2600 0.2059 0.6836 0.1865

0.7253 0.3736 1.1342 0.2736

0.2412 0.2377 0.2103 0.2427 0.2416 0.5999

0.0415 0.0321 0.0418 0.2141

0.8153 0.7557 0.1248

0.5379 0.3669 0.3708 0.0557 0.1044 0.2854 0.1945 0.4687 0.1211 0.5207 0.4099

0.4267 0.2330 0.3833

1.2563 2.0425 2.0278 11.9349 14.3196

Q25

0.5226

0.3830 0.8572 0.8166 1.4907 0.7658 0.8843 0.9587

0.6999 0.1714 0.4076 0.2048 0.3745 0.6441 0.2931 0.3463 0.2517 0.9159 0.2558

0.8326 0.5916 1.2531 0.3727

0.3816 0.3850 0.3299 0.4244 0.3861 0.8504

0.0724 0.0472 0.0587 0.3289

0.9790 0.8154 0.1717

0.6558 0.4839 0.4503 0.1000 0.1480 0.3558 0.2202 0.5888 0.1374 0.6592 0.5113

0.7053 0.3200 0.6537

1.3574 2.5674 2.3083 >1 × 106 207.0945

Med

TimesFM

1.0152

0.4636 1.0138 0.9885 1.7835 0.8686 1.0615 1.3614

1.3935 0.2389 0.5787 0.2654 0.4451 0.8880 0.3926 0.4705 0.3311 1.8321 0.3119

0.9860 1.5772 1.5306 0.5817

0.6337 0.5624 0.5684 0.7662 0.8238 1.6566

0.1082 0.1624 0.0815 0.5885

1.2495 0.9126 0.2632

0.8383 0.6464 0.5802 0.1981 0.2607 0.4502 0.2719 0.8555 0.1701 0.8654 0.6913

1.2384 0.5256 1.3464

1.6917 3.1353 2.7310 >1 × 106 >1 × 106

Q75

>1 × 106

2.8461 4.6902 9.7114 8.4683 5.8021 5.1621 13.9566

921.9849 0.6714 10.8124 1.0604 0.9651 4.5963 1.1025 2.9401 0.8309 19.7730 1.2802

6.9783 >1 × 106 11.1042 8.1760

2.2865 2.4969 7.9338 10.6721 13.8733 12.1920

0.5212 1.4407 0.2987 4.7434

4.7754 3.9889 0.7748

4.0308 2.1113 >1 × 106 0.9098 1.7904 5.0338 3.2251 15.6559 2.4933 6.4892 4.4615

7.8946 4.1642 14.0379

4.8600 13.0484 22.8176 >1 × 106 >1 × 106

Max

Table B.8: Results Covariate Benchmark: Statistics (Min, Q25, Median, Q75, Max) over multiple forecast horizons and context lengths; best median per row highlighted. Overall row aggregates globally across all datasets, targets, horizons, and context lengths. Values > 106 are treated as diverged, unusable forecasts and displayed as > 106 .

All

Overall

Summary (Best Med)

10 random aggregated households random_household_0 random_household_1 random_household_2 NO_PV_SFH10_P_TOT NO_PV_SFH31_P_TOT WITH_PV_SFH15_P_TOT

Aggregated Solar Solar Wind Offshore Wind Onshore Solar Solar_MWh_credit total_MWh_credit Wind_MWh_credit Solar active_power generation_kwh_UG Hall4

Total Power 50 Agg Total Power Total Power 50 Agg Aggregated Profile 107

LMP NP15 LMP SP15 LMP ZP26 Day-Ahead Auction Intraday Continuous reBAP

Aggregated Load Load DE Load 2 random loads

Heatpump 818882 Heatpump 971151 Heat Demand

Aggregated Batterys Fossil Gas Fossil Hard Coal

Area Control Error (NRV Saldo) Germany aFRR negativ Germany aFRR positiv TenneT negativ TenneT positiv

Target

HTW Berlin Households HTW Berlin Households HTW Berlin Households HTW Berlin Households Household Lower Saxony Household Lower Saxony Household Lower Saxony

Residential Load

Non-Dispatchable Generation

Mobilitaet Public Charging Station NL Office EV Park UK Residential Charging Station UrbanEV China Charging Station

Mobility Data

California Caiso California Caiso California Caiso ENTSO-E Germany ENTSO-E Germany ENTSO-E Germany

Market Data

California Caiso DE Power FR Power Industrial VEA 2 Agg Profiles

Load

HEAPO: Household Zurich Area HEAPO: Household Zurich Area Heat Grid Flensburg

Heat Data

Grid Data

California Caiso ENTSO-E Germany ENTSO-E Germany

Dispatchable Generation

Balancing Data Germany aFRR Germany aFRR Germany mFRR Germany mFRR Germany

Balancing Services

Dataset

All

Cal DE Cal DE Cal DE Cal DE Cal DE Cal DE Cal DE

DE Cal NL Cal UK Cal CN Cal

Weather NP15, Cal California Weather SP15, Cal California Weather ZP26, Cal California DE Weather + Calendar DE Weather + Calendar DE Weather + DE Cal

Weather NP15, SP15, ZP26, Cal California DE Weather + Calendar FR Weather DE Calendar

Zurich Weather + CH Cal Zurich Weather + CH Cal Weather + DE Cal

Weather NP15, SP15, ZP26, Cal California Wind + DE Weather + Cal Wind Weather + Calendar

DE Weather + Calendar DE Weather + Calendar DE Weather + Calendar DE Weather + Calendar DE Weather + Calendar

Covariates

0.0058

0.1843 0.3497 0.2313 0.2365 0.1404 0.1782 0.2480

0.0338 0.0614 0.1341 0.0769 0.2350 0.2458 0.0668 0.0176 0.0626 0.3141 0.0400

0.5464 0.1004 0.9021 0.0641

0.0660 0.0642 0.0627 0.0610 0.0643 0.2596

0.0090 0.0078 0.0058 0.0614

0.3477 0.4382 0.0703

0.5020 0.1997 0.1956 0.0134 0.0278 0.0999 0.1135 0.1629 0.0779 0.1457 0.1684

0.1359 0.0626 0.0665

1.0315 1.4073 1.3608 5.0229 3.3259

Min

0.2709

0.3157 0.7288 0.6303 1.1679 0.6399 0.7175 0.5280

0.2789 0.1832 0.5583 0.4018 0.4508 0.5786 0.2901 0.3563 0.1881 0.9834 0.2456

0.6772 1.0896 1.1697 0.2503

0.1941 0.2017 0.1899 0.2547 0.1981 0.4879

0.0567 0.0656 0.0432 0.3358

0.7575 0.7157 0.1157

0.8638 0.4998 0.4955 0.0736 0.1186 0.2410 0.1630 0.5655 0.1147 0.3689 0.3366

0.3762 0.2890 0.4131

1.1861 1.9114 2.0143 9.9741 9.8012

Q25

0.6168

0.4002 0.8287 0.8058 1.4445 0.7276 0.8593 0.7220

1.5877 0.2711 0.6953 0.5518 0.5359 0.8674 0.4680 0.5664 0.2631 1.3252 0.6515

0.7499 1.7093 1.2738 0.3430

0.2989 0.3178 0.2736 0.3912 0.3466 0.6601

0.1265 0.1653 0.0951 0.5213

0.8539 0.7934 0.1376

1.1033 0.6297 0.6307 0.1541 0.2176 0.3585 0.1965 0.8624 0.1410 0.5901 0.4983

1.6562 0.4785 0.7066

1.2369 2.2529 2.2225 >1 × 106 >1 × 106

Med

Q75

1.0564

0.4820 0.9361 0.9107 1.6705 0.8177 0.9921 1.0056

3.4043 0.3740 0.9130 0.7187 0.7082 1.3596 0.6257 0.8407 0.3839 1.5607 1.0307

0.8678 2.9204 1.3781 0.4351

0.6299 0.6935 0.5647 0.5668 0.6223 1.0332

0.1703 0.1971 0.1220 0.6792

0.9913 0.8931 0.1818

1.3126 0.7664 0.7676 0.2218 0.3083 0.4758 0.2268 1.1525 0.1638 0.8592 0.7090

2.3452 0.6659 1.0668

1.2706 2.5930 2.3546 >1 × 106 >1 × 106

Chronos-2

0.2361 0.3838 0.2985 0.8318 0.3376 0.6037 0.3021 0.0000

>1 × 106

0.0148 0.1271 0.1170 0.0961 0.2687 0.2017 0.0309 0.0110 0.1088 0.4215 0.1094

0.5327 0.1854 0.9485 0.0767

0.0634 0.0625 0.0365 0.0448 0.1805 0.3047

0.0336 0.0136 0.0175 0.0612

0.6341 0.7755 0.0734

0.2779 0.2631 0.2624 0.0290 0.0676 0.1617 0.1572 0.2383 0.0960 0.3419 0.2453

0.1919 0.1180 0.0552

1.1397 1.2130 1.3778 4.9390 0.0000

Min

0.7512 1.4130 1.2085 2.0409 0.9810 1.3005 1.5282

2316.4590 0.9214 16.9366 1.9142 1.5437 4.5811 1.3451 4.6669 0.7947 3.7004 6.7483

1.0676 >1 × 106 2.5616 1.0110

5.0033 3.8426 5.4946 12.3767 12.7509 3.1974

0.3396 0.2583 0.1743 1.8948

1.5154 1.3936 0.4630

4.6604 1.3424 >1 × 106 0.3023 0.5613 0.9973 0.3228 2.4649 0.2131 1.4526 1.3556

9.1685 1.3783 7.2209

1.3583 3.9312 3.0507 >1 × 106 >1 × 106

Max

0.3434

0.3515 0.8677 0.6808 1.1716 0.7891 1.0496 0.6526

0.7148 0.3544 0.4288 0.4424 0.4652 0.4619 0.3021 0.2989 0.3075 0.8503 0.2528

0.7866 0.5778 1.2088 0.2927

0.2097 0.2193 0.2045 0.4049 0.3843 0.5182

0.0896 0.0298 0.0518 0.2031

0.9581 0.9249 0.1430

0.4770 0.4983 0.5066 0.1094 0.2194 0.4220 0.2163 0.4734 0.1669 0.9572 0.6103

1.0401 0.3353 0.4194

1.2369 1.9432 1.9034 142.3116 148.7303

Q25

0.6587

0.3908 1.0435 0.7886 1.3281 0.9168 1.2947 0.8822

1.2632 0.5098 0.6644 0.6136 0.6271 0.6849 0.3739 0.4213 0.4436 1.1840 0.3338

0.8876 0.8431 1.3660 0.3653

0.3946 0.3706 0.3515 0.6568 0.5748 0.7205

0.1171 0.0394 0.0792 0.2578

1.2076 0.9968 0.1800

0.5969 0.6309 0.6535 0.1791 0.2980 0.5869 0.2469 0.7544 0.2232 1.2188 0.8908

1.3271 0.4174 0.6393

1.2683 2.5026 2.1612 >1 × 106 9930.4413

Med

Q75

1.1655

0.4405 1.2834 0.8736 1.5237 1.0180 1.8288 1.0913

1.7622 0.7321 0.9835 0.8085 0.7893 0.8503 0.5070 0.6446 0.6368 1.7246 0.4909

1.0695 1.8656 1.5732 0.4800

0.6250 0.6073 0.5761 1.1737 0.8878 1.2983

0.1467 0.0667 0.1059 0.3890

1.3976 1.0789 0.2977

0.7257 0.8446 0.8735 0.2818 0.4136 0.8725 0.3005 1.0632 0.2583 1.4733 1.1614

1.7499 0.5283 0.9879

1.3020 3.4147 2.4650 >1 × 106 >1 × 106

RandomForest

>1 × 106

0.6296 2.3120 1.1610 3.6669 1.6981 3.7198 2.8475

66.2516 1.7325 4.6994 2.6016 1.5862 2.9353 1.1862 3.2346 0.8720 9.1513 1.1939

1.7092 >1 × 106 3.2447 1.1299

3.1464 3.9737 3.1484 14.2649 7.5323 10.7840

0.2796 0.1886 0.2086 0.9809

2.1057 1.7813 2.6712

2.3695 3.3814 >1 × 106 0.5127 0.6520 1.3095 0.4917 2.3041 0.3439 2.3061 1.6359

4.0102 1.0413 3.9918

1.3900 7.7331 7.3007 >1 × 106 >1 × 106

Max

0.0083

0.2436 0.3674 0.3192 0.8694 0.5834 0.6875 0.3883

0.0396 0.0893 0.1164 0.1062 0.2729 0.2392 0.0413 0.0148 0.0608 0.2429 0.0934

0.5522 0.1955 1.0137 0.0986

0.0777 0.1008 0.0923 0.0900 0.1688 0.2770

0.0083 0.0106 0.0153 0.0841

0.6904 0.7573 0.0607

0.2636 0.2085 0.1991 0.0252 0.0709 0.1314 0.1425 0.1990 0.0905 0.3351 0.1893

0.0816 0.0778 0.0794

1.1210 1.2115 1.3966 4.9793 3.1876

Min

0.3193

0.3516 0.8112 0.7678 1.3797 0.8467 1.2372 0.7696

0.3925 0.2674 0.4116 0.2998 0.4497 0.4822 0.2745 0.2951 0.2314 0.6525 0.2379

0.7667 0.5120 1.2614 0.2969

0.2910 0.3463 0.2979 0.3674 0.4937 0.5561

0.0375 0.0248 0.0412 0.1994

0.9181 0.9419 0.1051

0.4751 0.4238 0.4047 0.1025 0.1803 0.3284 0.2136 0.4029 0.1186 0.7865 0.5170

0.3672 0.2762 0.3546

1.2303 1.9635 1.9324 10.4132 16.4038

Q25

0.6026

0.3955 0.9997 0.8661 1.6437 0.9113 1.5531 0.9611

0.9598 0.4077 0.6479 0.3839 0.5842 0.6810 0.3450 0.4409 0.3219 0.8158 0.3017

0.8642 0.7511 1.3316 0.3662

0.5032 0.5333 0.4986 0.5571 0.9295 0.7663

0.0624 0.0330 0.0607 0.2518

1.1972 0.9900 0.1336

0.6041 0.5665 0.5438 0.1727 0.2616 0.4820 0.2436 0.4887 0.1301 0.9904 0.6475

0.5876 0.3470 0.5346

1.2616 2.6146 2.1804 >1 × 106 >1 × 106

Med

Q75

1.0996

0.4546 1.3161 0.9524 1.9906 0.9679 2.0152 1.1948

1.6078 0.5640 0.9185 0.4896 0.7546 0.8785 0.4345 0.5813 0.4625 1.1684 0.4115

1.0344 1.2441 1.4493 0.4738

0.9329 0.8073 0.7651 1.1785 1.5435 1.5230

0.0877 0.0422 0.0909 0.4050

1.4055 1.0441 0.2140

0.7319 0.8102 0.7998 0.2741 0.4785 0.6543 0.2806 0.6449 0.1460 1.2351 0.7822

0.9264 0.4435 0.8458

1.2918 3.7036 2.6241 >1 × 106 >1 × 106

XGBoost

>1 × 106

1.0291 2.3555 1.5626 5.7324 1.3373 4.6220 2.2769

1720.7720 1.0320 4.6151 1.1258 1.5366 2.8173 1.3514 1.9037 0.7720 10.8274 1.2580

1.6603 >1 × 106 2.1444 1.0347

20.5536 5.6083 4.6540 7.4026 23.2747 13.5733

0.2416 0.0991 0.2323 1.1366

2.2991 1.5257 1.1000

2.8345 3.1807 >1 × 106 0.4663 0.8030 0.9683 0.4565 1.2441 0.1959 1.9582 1.5450

4.0855 0.7188 2.7132

1.4931 11.2826 7.5942 >1 × 106 >1 × 106

Max

Table B.9: Results Training Benchmark: Statistics (Min, Q25, Median, Q75, Max) over multiple forecast horizons and context lengths; best median per row highlighted. Overall row aggregates globally across all datasets, targets, horizons, and context lengths. Values > 106 are treated as diverged, unusable forecasts and displayed as > 106 .

Record · ID 134595 · SHA-256 26de18595c72447f
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