# Deep Time-series Forecasting Needs Kernelized Moment Balancing

arXiv: https://arxiv.org/abs/2602.00717 · HTML: https://mlsanity.com/paper/2602.00717/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 58 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 30 of 36)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting](https://mlsanity.com/paper/2410.04442/) (2024)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [Unlocking the Power of LSTM for Long Term Time Series Forecasting](https://mlsanity.com/paper/2408.10006/) (2024)
- [MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model](https://mlsanity.com/paper/2409.07486/) (2024)
- [OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain](https://mlsanity.com/paper/2505.08550/) (2025)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment](https://mlsanity.com/paper/2510.24574/) (2025)

## Built on by (most cited first, 2 of 2)

- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [CoRe: Coherence and Relational Alignment for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2609.19670/) (2026)

## Abstract (arXiv)

Deep time-series forecasting can be formulated as a distribution balancing problem aimed at aligning the distribution of the forecasts and ground truths. According to Imbens' criterion, balancing two distributions requires that their first moments be identical with respect to any balancing function. We demonstrate that existing objectives enforce moment matching only for one or two predefined balancing functions, thus failing to achieve full distribution balance. To address this limitation, we propose direct forecasting with kernelized moment balancing (KMB-DF). Unlike existing objectives, KMB-DF adaptively selects the most informative balancing functions from a reproducing kernel Hilbert space (RKHS) to enforce sufficient distribution balancing. A tractable and differentiable formulation is derived to enable estimation from empirical samples and seamless integration into gradient-based training pipelines. Extensive experiments across multiple models and datasets show that KMB-DF consistently improves forecasting accuracy and achieves state-of-the-art performance. Code is available at https://anonymous.4open.science/r/KMB-DF-403C.