Financial market forecasting is inherently uncertain, yet most deep learning approaches rely on point predictions that provide only single-value estimates without quantifying uncertainty. Such predictions are insufficient for risk-aware decision-making, as they fail to capture the range of possible outcomes and the associated confidence of forecasts.The problem can be solved using prediction intervals, which allow obtaining an upper and lower bound for the prediction, thus enabling uncertainty representation in the model. Yet, the current methods tend to disregard relationships between assets or cannot simultaneously ensure good calibration and sharpness of the resulting intervals in dynamically changing market regimes. In our work, we propose a spatio-temporal graph-based approach with a bi-level chaotic fusion technique to solve this problem. Our model uses separate nonlinear transformation functions to estimate the interval center and width. Additionally, a volatility-aware gating mechanism is used to make predictions dependent on the regime in which the market operates. Temporal dependencies are considered by embedding graph structures and sequentially modeling them. Training is conducted according to a Lower-Upper Bound Estimation (LUBE) objective. Our experimental results show significant improvements compared to existing baselines (LSTM, GRU, GCN, HGNN) when applied to data from 2016 to 2026 with 43 leading companies in eight sectors of the NSE. It provides the lowest Winkler score (0.0778), tightest prediction intervals (PIAW = 0.1407), and highest coverage (PICP = 96.6%), with all differences statistically significant (p < 0.001) according to the Diebold-Mariano test.

翻译：金融市场预测具有固有的不确定性，但大多数深度学习方法依赖点预测，仅提供单值估计而无法量化不确定性。此类预测不足以支持风险感知决策，因为它们无法捕捉可能的结果范围及预测的置信度。预测区间可解决该问题，通过提供预测的上限和下限，从而在模型中实现不确定性表示。然而，现有方法往往忽略资产间的关系，或在动态变化的市场机制中无法同时确保所得区间的良好校准性与锐度。本研究提出一种基于时空图的方法，结合双层混沌融合技术以解决此问题。该模型使用独立的非线性变换函数来估计区间中心与宽度，并引入波动感知门控机制，使预测依赖于市场运行状态。通过嵌入图结构并对其进行序列建模来考虑时间依赖性，训练过程遵循下界-上界估计（LUBE）目标。实验结果表明，与现有基线方法（LSTM、GRU、GCN、HGNN）相比，该方法在2016年至2026年印度国家证券交易所（NSE）八大板块43家领先公司的数据上表现显著提升：获得最低Winkler评分（0.0778）、最紧凑预测区间（PIAW=0.1407）及最高覆盖度（PICP=96.6%），且根据Diebold-Mariano检验所有差异均具有统计显著性（p < 0.001）。