# SPECTRA: State-Space Exogenous Context and Temporal-Frequency Resolution Architecture for Probabilistic Energy Forecasting

arXiv: https://arxiv.org/abs/2607.20587 · HTML: https://mlsanity.com/paper/2607.20587/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [CRPS Learning](https://mlsanity.com/paper/2102.00968/) (2021)
- [Open Power System Data - Frictionless data for electricity system modelling](https://mlsanity.com/paper/1812.10405/) (2018)
- [Electricity Demand and Grid Impacts of AI Data Centers: Challenges and Prospects](https://mlsanity.com/paper/2509.07218/) (2025)
- [Adaptive Probabilistic Forecasting of Electricity (Net-)Load](https://mlsanity.com/paper/2301.10090/) (2023)
- [Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems](https://mlsanity.com/paper/2409.07637/) (2024)
- [Attention-based Neural Load Forecasting: A Dynamic Feature Selection Approach](https://mlsanity.com/paper/2108.11763/) (2021)
- [DiffLoad: Uncertainty Quantification in Electrical Load Forecasting with the Diffusion Model](https://mlsanity.com/paper/2306.01001/) (2023)
- [KARMA: A Multilevel Decomposition Hybrid Mamba Framework for Multivariate Long-Term Time Series Forecasting](https://mlsanity.com/paper/2506.08939/) (2025)

## Abstract (arXiv)

Modern power systems increasingly require probabilistic forecasts amid interacting uncertainties from renewable intermittency, flexible demand, market volatility, and weather-dependent generation. However, existing methods often treat multi-scale decomposition, exogenous-variable alignment, and probabilistic output as separate steps, obscuring how predictable structures and uncertainty-bearing fluctuations jointly shape the forecast distribution. This paper proposes a state-space exogenous-context and temporal-frequency resolution architecture for general probabilistic energy forecasting. Its central premise is that trend-periodic components primarily determine the baseline trajectory, whereas high-frequency residuals and external perturbations govern the spread and asymmetry of forecast uncertainty. Accordingly, the architecture adaptively separates deterministic and residual streams, aligns exogenous context with both, refines the deterministic backbone through multi-resolution spectral-temporal state-space modeling, and estimates ordered quantile boundaries from their complementary representations. Experiments on load, price, solar, and wind forecasting achieve the best continuous ranked probability score in 14 of 18 settings, reducing average CRPS by 5.74% and upper-tail quantile risk by 7.27% over the strongest baselines. These results support deterministic-stochastic separation as an effective design principle for general probabilistic energy forecasting.