# Mamba time series forecasting with uncertainty quantification

arXiv: https://arxiv.org/abs/2503.10873 · HTML: https://mlsanity.com/paper/2503.10873/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 20 of its 62 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [An Experimental Review on Deep Learning Architectures for Time Series Forecasting](https://mlsanity.com/paper/2103.12057/) (2021)
- [MambaStock: Selective state space model for stock prediction](https://mlsanity.com/paper/2402.18959/) (2024)
- [A Mamba Foundation Model for Time Series Forecasting](https://mlsanity.com/paper/2411.02941/) (2024)
- [A Co-training Approach for Noisy Time Series Learning](https://mlsanity.com/paper/2308.12551/) (2023)
- [Sequential Monte Carlo Learning for Time Series Structure Discovery](https://mlsanity.com/paper/2307.09607/) (2023)
- [Non-parametric Probabilistic Time Series Forecasting via Innovations Representation](https://mlsanity.com/paper/2306.03782/) (2023)
- [Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve](https://mlsanity.com/paper/2501.08288/) (2025)

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

- [FEG-Pro: Forecast-Error Growth Profiling for Finite-Horizon Instability Analysis of Nonlinear Time Series](https://mlsanity.com/paper/2605.17282/) (2026)
- [Beyond Static Uncertainty: Modeling Temporal Uncertainty Dynamics for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2603.24254/) (2026)

## Abstract (arXiv)

State space models, such as Mamba, have recently garnered attention in time series forecasting due to their ability to capture sequence patterns. However, in electricity consumption benchmarks, Mamba forecasts exhibit a mean error of approximately 8%. Similarly, in traffic occupancy benchmarks, the mean error reaches 18%. This discrepancy leaves us to wonder whether the prediction is simply inaccurate or falls within error given spread in historical data. To address this limitation, we propose a method to quantify the predictive uncertainty of Mamba forecasts. Here, we propose a dual-network framework based on the Mamba architecture for probabilistic forecasting, where one network generates point forecasts while the other estimates predictive uncertainty by modeling variance. We abbreviate our tool, Mamba with probabilistic time series forecasting, as Mamba-ProbTSF and the code for its implementation is available on GitHub (https://github.com/PessoaP/Mamba-ProbTSF). Evaluating this approach on synthetic and real-world benchmark datasets, we find Kullback-Leibler divergence between the learned distributions and the data--which, in the limit of infinite data, should converge to zero if the model correctly captures the underlying probability distribution--reduced to the order of 10-3 for synthetic data and 10-1 for real-world benchmark, demonstrating its effectiveness. We find that in both the electricity consumption and traffic occupancy benchmark, the true trajectory stays within the predicted uncertainty interval at the two-sigma level about 95% of the time. We end with a consideration of potential limitations, adjustments to improve performance, and considerations for applying this framework to processes for purely or largely stochastic dynamics where the stochastic changes accumulate, as observed for example in pure Brownian motion or molecular dynamics trajectories.