# HAN-Mamba: Hierarchical Selective State Space Networks for Multi-Scale Financial Volatility Forecasting

arXiv: https://arxiv.org/abs/2610.10323 · HTML: https://mlsanity.com/paper/2610.10323/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 2 of its 32 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## 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, 2 of 2)

- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Volatility forecasting using Deep Learning and sentiment analysis](https://mlsanity.com/paper/2210.12464/) (2022)

## Abstract (arXiv)

Short-horizon realized volatility forecasting requires the integration of market information that evolves at incompatible temporal resolutions, from second-level order book dynamics to weekly regime drift. Our conference work introduced HAN-T, a hierarchical architecture in which scale-specific Transformer encoders process short, mid, and long-horizon streams and a learned attention fuser weighs their contributions. This article replaces the quadratic attention encoders with selective state space (Mamba) encoders while retaining attention only in the fuser, where the input is a three-token set rather than a long sequence. The resulting hybrid, HAN-Mamba, summarizes each stream through a recurrent state whose input-dependent gating matches two structural properties of volatility: persistent but decaying memory and abrupt regime shifts. On the Optiver Realized Volatility Prediction benchmark under time-aware five-fold cross-validation, HAN-Mamba improves mean RMSPE over HAN-T (0.1942 vs. 0.1965) with 33% fewer parameters. Its linear-time encoders further allow the high-frequency context to be extended from 60 to 240 buckets, reducing error to 0.1927 where the attention variant saturates, and support constant-time streaming updates at inference. Ablations attribute the gains to the encoder swap, confirm that the hierarchical prior transfers across sequence-model families, and show that the permutation-invariant attention fuser remains the correct mechanism for cross-scale integration.