Bi-Level Chaotic Fusion Based Graph Convolutional Network for Stock Market Prediction Interval
Authors: Eshwar Sai Kandimalla, Sravan Chowdary Kankanala, Sumana Bhimineni, Hem Sundhar Korukunda, Vivek Yelleti
Organizations: Department of Computer Science & Engineering, SRM University AP, India
Abstract
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.
Stock price prediction remains challenging due to the non-stationary and noisy nature of financial time series. Existing deep learning models often rely on rigid decision-level fusion, ad hoc hyperparameter tuning, and compressed final-layer outputs, causing information loss, overfitting, and limited cross-market generalization. We propose VertiFuseX, a hybrid LSTM architecture using penultimate-layer vertical fusion of multi-scale temporal representations. VertiFuseX stacks and reweights penultimate features from LSTM, Bi-LSTM, and St-LSTM branches, integrates a parallel DNN stream, and jointly optimizes all components via backpropagation under a fixed hyperparameter configuration. This preserves richer intermediate temporal information across scales. Evaluated on 15 years (2010-2024) of closing prices from 10 global equity indices using strict chronological out-of-sample testing with the final 365 trading days held out, VertiFuseX achieves 30-54% MAPE reductions and over 40% improvements in MAE and RMSE versus LSTM-based baselines, and outperforms seven state-of-the-art models across 33 metric-dataset comparisons. Ablation studies confirm penultimate-layer fusion drives these gains over final-layer fusion and decision-level ensembling. Gradient-based saliency analysis shows consistent emphasis on mid-range dependencies at lags 9-15 days. Economic validation via algorithmic trading simulation under extreme market regimes shows reduced maximum drawdowns and superior risk-adjusted returns. With 675k parameters, a 2.6 MB memory footprint, and 1.5 ms/sample inference latency, VertiFuseX offers a lightweight, interpretable, deployment-ready framework for robust financial forecasting.
The quantification of uncertainty in prediction models is crucial for reliable decision-making, yet remains a significant challenge. Interval time series forecasting offers a principled solution to this problem by providing prediction intervals (PIs), which indicates the probability that the true value falls within the predicted range. We consider a recently established point forecasts (PFs) method termed Learning-Based Convolution Nuclear Norm Minimization (LbCNNM), which directly generates multi-step ahead forecasts by leveraging the convolutional low-rankness property derived from training data. While theoretically complete and empirically effective, LbCNNM lacks inherent uncertainty estimation capabilities, a limitation shared by many advanced forecasting methods. To resolve the issue, we modify the well-known Quantile Regression (QR) and integrate it into LbCNNM, resulting in a novel interval forecasting method termed LbCNNM with Modified Quantile Regression (LbCNNM-MQR). In addition, we devise interval calibration techniques to further improve the accuracy of PIs. Extensive experiments on over 100,000 real-world time series demonstrate the superior performance of LbCNNM-MQR.
Uncertainty quantification (UQ) in graph neural networks (GNNs) is crucial in high-stakes domains but remains a significant challenge. In graph settings, message passing often relies on strong assumptions such as exchangeability, which are rarely satisfied in practice, and achieving reliable UQ typically requires costly resampling or post-hoc calibration. To address these issues, we introduce Quantile-free Prediction Interval GNN (QpiGNN), a framework that builds on quantile regression (QR) to enable GNN-based UQ by directly optimizing coverage and interval width without requiring quantile inputs or post-processing. QpiGNN employs a dual-head architecture that decouples prediction and uncertainty, and is trained with label-only supervision through a quantile-free joint loss. This design allows efficient training and yields robust prediction intervals, with theoretical guarantees of asymptotic coverage and near-optimal width under mild assumptions. Experiments on 19 synthetic and real-world benchmarks show QpiGNN achieves average 22% higher coverage and 50% narrower intervals than baselines, while ensuring efficiency and robustness to noise and structural shifts.