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arxiv: 2605.16324 · v1 · pith:SQWIB7D6new · submitted 2026-05-05 · 💻 cs.LG · cs.CE· q-fin.ST

Bi-Level Chaotic Fusion Based Graph Convolutional Network for Stock Market Prediction Interval

Eshwar Sai Kandimalla , Sravan Chowdary Kankanala , Sumana Bhimineni , Hem Sundhar Korukunda , Vivek Yelleti This is my paper

Pith reviewed 2026-05-21 00:30 UTC · model grok-4.3

classification 💻 cs.LG cs.CEq-fin.ST
keywords prediction intervalsgraph convolutional networkstock market forecastingchaotic fusionvolatility-aware gatinguncertainty quantificationNSE data
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The pith

A bi-level chaotic fusion graph model produces tighter and better-calibrated prediction intervals for stock prices than standard LSTM, GRU, and GCN baselines.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to replace single-value stock forecasts with prediction intervals that bound possible future prices and express their uncertainty. It builds a graph convolutional network in which bi-level chaotic fusion applies separate nonlinear maps to compute interval center and width, while a volatility-aware gate adjusts the flow of information according to current market conditions. Relationships among stocks are encoded as graph edges and processed sequentially so that temporal patterns reflect both asset interdependencies and regime shifts. The network is trained by minimizing a lower-upper bound estimation loss. When evaluated on daily data for 43 major companies across eight sectors of the National Stock Exchange from 2016 to 2026, the resulting intervals record the lowest Winkler score, the smallest average width, and the highest coverage probability, all differences reaching statistical significance against the listed baselines.

Core claim

The central claim is that embedding stock relationships in a graph, fusing chaotic nonlinear transformations at two levels to set interval bounds, and gating the temporal updates by volatility produces prediction intervals that are simultaneously sharp and well-calibrated for financial time series.

What carries the argument

Bi-level chaotic fusion inside graph convolutional layers, which uses two distinct nonlinear transformation functions to estimate the center and width of each prediction interval together with a volatility-aware gating mechanism that conditions the recurrence on the prevailing market regime.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same fusion-plus-gating pattern could be tested on other networked financial series such as commodity prices or currency pairs where assets also influence one another.
  • Adding macroeconomic nodes to the graph might let the intervals reflect external shocks without changing the core training objective.
  • Real-time deployment on live order-book data would reveal whether the interval widths remain useful for setting dynamic risk limits during intraday trading.

Load-bearing premise

That the graph of 43 selected stocks and the volatility patterns observed between 2016 and 2026 are representative enough for the fusion and gating steps to generalize without overfitting to that particular market slice.

What would settle it

Retraining the model on an earlier decade (for example 2005-2015) or on a different exchange and finding that the Winkler score and coverage advantages disappear or lose statistical significance would falsify the claim that the architecture reliably captures regime-dependent dependencies.

Figures

Figures reproduced from arXiv: 2605.16324 by Eshwar Sai Kandimalla, Hem Sundhar Korukunda, Sravan Chowdary Kankanala, Sumana Bhimineni, Vivek Yelleti.

Figure 1
Figure 1. Figure 1: Architecture of LSTM Gated Recurrent Unit Gated Recurrent Units (GRUs) are advanced recurrent neural networks that are used to capture the temporal dynamics in a more efficient manner using a gating mechanism [17]. In contrast to long short-term memory (LSTM) neural networks, the GRU model is a simpler structure because it combines both input and forget gates to one update gate. In every time instant t, th… view at source ↗
Figure 2
Figure 2. Figure 2: Architecture of GRU Graph Convolution network Graph Convolutional Networks (GCNs) generalize convolution to graph-based data structures that facilitate learning on non-Euclidean spaces [14]. The graph structure G=(V,E) consists of nodes representing entities and edges denoting relations among these entities. Within finance, stock assets can be considered as nodes while the edges can be considered as correl… view at source ↗
Figure 3
Figure 3. Figure 3: Architecture of BCF-GCN [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graph representaƟon learning using the correlaƟon graph. The stocks are nodes, while edges are formed based on a condiƟon whereby the returns of the stock correlaƟon is above a threshold value. Note : BANKi indicates the ith bank, while BANK, IT, PHARMA, and ENERGY are stocks of respecƟve sectors. 4.4 Bi-Level Chaotic Transformation Layer In this layer, we utilize both the logistic and tent chaotic maps to… view at source ↗
Figure 3
Figure 3. Figure 3: Logistic and tent maps used in the bi-level chaotic fusion design. [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Gating and interval generation logic [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: Data Preprocessing Pipeline [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 8
Figure 8. Figure 8: Coverage-width trade-off showing BCF-GCN as the sharpest covered model [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Ablation study: impact of component removal on PIAW and Winkler score [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Ablation study heatmap showing relative performance across metrics [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Mean Winkler score across multi-seed testing. [PITH_FULL_IMAGE:figures/full_fig_p030_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Backtesting SMAPE results [PITH_FULL_IMAGE:figures/full_fig_p032_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Diebold-Mariano significance results [PITH_FULL_IMAGE:figures/full_fig_p032_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: Example Prediction Interval for high-priced stocks [PITH_FULL_IMAGE:figures/full_fig_p034_12.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript presents a Bi-Level Chaotic Fusion Based Graph Convolutional Network for generating prediction intervals in stock market forecasting. The model incorporates graph structures to capture inter-asset relationships, uses nonlinear transformations for interval center and width, a volatility-aware gating mechanism for regime dependence, and is trained using the Lower-Upper Bound Estimation (LUBE) objective. Experiments on data from 43 leading companies in the NSE from 2016 to 2026 demonstrate improved performance over baselines like LSTM, GRU, GCN, and HGNN, with the lowest Winkler score of 0.0778, PIAW of 0.1407, PICP of 96.6%, and statistically significant differences (p < 0.001) per the Diebold-Mariano test.

Significance. If the empirical results are robust to proper temporal validation and graph construction without lookahead bias, this work could contribute to better uncertainty quantification in financial time series by integrating spatio-temporal modeling with chaotic fusion and regime-aware gating. The approach addresses a relevant problem in risk-aware decision making.

major comments (3)
  1. [Experimental Setup] The paper does not specify how the graph adjacency matrix is constructed. If it is based on correlations computed over the full 2016-2026 period, this would introduce lookahead bias, as future data informs the graph used for earlier time steps, potentially inflating the reported PICP and sharpness metrics.
  2. [Results] No error bars, standard deviations, or confidence intervals are provided for the reported metrics (Winkler score, PIAW, PICP). This makes it difficult to evaluate the practical significance of the improvements and the reliability of the Diebold-Mariano test results.
  3. [Methods] There is no discussion of data leakage prevention, such as using rolling window validation or ensuring the graph is constructed only on training data. This is critical for time series forecasting claims.
minor comments (2)
  1. [Abstract] The abstract mentions 'bi-level chaotic fusion technique' but does not provide a brief explanation of what this entails.
  2. [Notation] The definitions of interval center and width transformations could be clarified with equations for better reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback. The comments highlight important aspects of temporal integrity and reporting that we will address through revisions to strengthen the manuscript. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Experimental Setup] The paper does not specify how the graph adjacency matrix is constructed. If it is based on correlations computed over the full 2016-2026 period, this would introduce lookahead bias, as future data informs the graph used for earlier time steps, potentially inflating the reported PICP and sharpness metrics.

    Authors: We agree that the manuscript should have explicitly described the adjacency matrix construction to preclude any concern of lookahead bias. In our experiments the graph was formed using Pearson correlations computed only on the training window data for each prediction step, with edges retained above a fixed threshold. We will revise the Methods section to provide the precise construction formula, the threshold value, and confirmation that the process is repeated independently for every training fold using exclusively in-sample observations. revision: yes

  2. Referee: [Results] No error bars, standard deviations, or confidence intervals are provided for the reported metrics (Winkler score, PIAW, PICP). This makes it difficult to evaluate the practical significance of the improvements and the reliability of the Diebold-Mariano test results.

    Authors: This observation is correct and we will remedy it. The original experiments were repeated across five independent random seeds; we will now report mean values accompanied by standard deviations for all metrics and will add these statistics to the result tables. We will also include a brief discussion of the observed variability to support interpretation of the Diebold-Mariano test outcomes. revision: yes

  3. Referee: [Methods] There is no discussion of data leakage prevention, such as using rolling window validation or ensuring the graph is constructed only on training data. This is critical for time series forecasting claims.

    Authors: We acknowledge that an explicit description of leakage-prevention measures was omitted. Our protocol uses a rolling-window scheme in which both the training set and the adjacency matrix are updated at each step using only data available up to the end of the current training window. We will add a dedicated subsection in Experimental Setup that details the window length, stride, and the per-window graph reconstruction procedure, thereby documenting that temporal ordering is strictly preserved. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation chain self-contained against external benchmarks

full rationale

The abstract and described methods introduce a GCN-based model with bi-level chaotic fusion, volatility-aware gating, and LUBE training objective to produce prediction intervals. Standard evaluation metrics (Winkler score, PIAW, PICP) are applied post-training on held-out data from 2016-2026 NSE stocks, with comparisons to baselines. No equations or steps are visible that define a quantity in terms of itself, rename a fitted parameter as a prediction, or reduce the central claim to a self-citation chain. The graph construction and temporal modeling are presented as independent architectural choices whose performance is externally falsifiable via the reported statistical tests. This is the common honest finding for papers whose core contribution is an empirical architecture rather than a closed-form derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

Review performed on abstract only; concrete free parameters, axioms, and invented entities cannot be extracted. The abstract implies several modeling choices whose details are unavailable.

free parameters (2)
  • nonlinear transformation functions for interval center and width
    Separate functions are used to estimate center and width; their parameters are necessarily fitted to data.
  • volatility-aware gating parameters
    Gating mechanism depends on market regime and must be parameterized and trained.
axioms (1)
  • domain assumption Graph structures derived from asset relationships capture relevant spatio-temporal dependencies in stock returns
    Invoked when the model embeds graph structures to model temporal dependencies.
invented entities (1)
  • bi-level chaotic fusion technique no independent evidence
    purpose: To fuse information at two levels for improved interval estimation
    Introduced as a core component of the proposed architecture

pith-pipeline@v0.9.0 · 5842 in / 1519 out tokens · 52044 ms · 2026-05-21T00:30:53.817701+00:00 · methodology

discussion (0)

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Reference graph

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