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VertiFuseX: Generalizable Financial Forecasting via Multi-Stream Temporal Fusion
Aashish Bohra, Vivek Vijay
TL;DR
Stock forecasting remains difficult because financial time series are noisy and non-stationary, while existing models can compress temporal information and generalize poorly. VertiFuseX fuses penultimate-layer representations from multiple LSTM branches. It outperforms seven state-of-the-art models across 33 comparative evaluations and reports lower errors than LSTM-family baselines.
Problem
Stock price prediction is challenging because market data are non-stationary, high-dimensional, and noisy, while prior approaches exhibit decision-level fusion, tuning, and single-scale modeling limitations.
Source: §1 · p. 1Method
VertiFuseX combines LSTM, Bi-LSTM, and St-LSTM branches by vertically stacking and reweighting their penultimate-layer features before task-specific regression.
Source: §1 · pp. 2–3Results
VertiFuseX outperforms seven state-of-the-art models across 33 comparative evaluations and achieves up to 54.3% lower MAPE than LSTM-family baselines.
Source: §1 · p. 4, §6 · p. 39Takeaways & Limitations
The conclusion presents VertiFuseX as cross-market robust under the evaluated chronological protocols, with approximately 675k parameters and 1.5 ms/sample inference latency.
Source: §6 · p. 40The study does not use a full rolling-window walk-forward protocol, leaving aggregated performance across repeated regime transitions and formal cross-regime comparisons outside scope.
Source: §5.2 · p. 39
Abstract
from arXiv · showhide
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.
1 Introduction
Financial forecasting is challenged by noisy, non-stationary data and models that compress temporal information, overfit, or generalize poorly across markets. VertiFuseX addresses these issues with penultimate-layer fusion across temporal streams and evaluates forecasting under a chronological out-of-sample protocol.
Motivation
- The introduction identifies decision-level fusion, overfitting associated with ad hoc tuning, and single-scale temporal modeling as limitations in prior approaches.It argues that penultimate features retain more temporal structure than final outputs before fusion.Source: §1 · p. 2
VertiFuseX Architecture
- VertiFuseX vertically stacks penultimate features from LSTM, Bi-LSTM, and St-LSTM branches, then fuses them with non-temporal features from a parallel DNN stream.A learned affine transformation reweights the intermediate features before task-specific compression.Source: §1 · p. 3
Evaluation
- The evaluation uses 2010–2024 data from 10 global equity indices and reserves the final 365 trading days for chronological out-of-sample testing.The stated protocol is intended to prevent look-ahead bias and evaluate forward out-of-sample robustness under fixed parameters.Source: §1 · p. 3
Configuration and Efficiency
- A fixed, pre-validated hyperparameter configuration is used across indices, with a 20-day lookback, Adam at lr=10−4, ℓ2 regularization at 10−4, and dropout of 0.3.The model is reported to have 675k parameters, 1.5 ms/sample latency, and under 2-minute training per index.Source: §1 · p. 4
Performance Analysis
- Up to 54.3% lower MAPE and over 40% reductions in MAE and RMSE are reported against LSTM, Bi-LSTM, and St-LSTM baselines.Against state-of-the-art methods, the reported reductions reach 34.6% in MAE, 36.4% in RMSE, and 27.2% in MAPE across evaluated datasets.Source: §1 · p. 4
Economic Validation
- Stress tests during the COVID-19 crash and 2022 bear market show reduced maximum drawdowns and superior risk-adjusted returns versus passive and momentum benchmarks.Source: §1 · p. 4
2 Related Work
The related work is organized around temporal modeling strategies in deep-learning and hybrid forecasting. It identifies decision-level fusion, tuning demands, and implicit single-scale modeling as recurring limitations that motivate VertiFuseX’s penultimate-layer vertical fusion.
2.1 Deep Learning based Models
- Deep-learning approaches include recurrent, bidirectional, stacked, convolutional, and attention-based models, but evaluations often focus on few markets and temporal resolution remains largely fixed.The review notes tuning costs and limits in comparative depth or generalization for several approaches.Source: §2.1 · pp. 4–5
2.2 Hybrid Deep Learning based Models
- Hybrid models combine recurrent, convolutional, and ensemble components, yet examples retain tuning burdens, narrow evaluation, static fusion, or regime-adaptability concerns.Source: §2.2 · p. 5
- Prior hybrid designs generally treat multi-scale abstraction implicitly; the review identifies decision-level fusion, extensive tuning, and single-scale modeling as recurring limitations.VertiFuseX is presented as a hybrid LSTM framework using penultimate-layer vertical fusion and multi-scale abstraction; Table 1 is an illustrative, not comprehensive, comparison.Source: §2.2 · pp. 5–7
3 VertiFuseX: Proposed Methodology
This section presents VertiFuseX’s financial forecasting methodology, combining penultimate-layer representations from multiple temporal encoders with a parallel DNN stream through learned feature-level fusion. The fused features are jointly optimized and passed to regression.
3 VertiFuseX: Proposed Methodology
- The proposed scheme is organized into DATAETL, feature extraction, and vertical fusion, carrying the data from preprocessing through feature integration to prediction.The architecture includes LSTM, Bi-LSTM, and St-LSTM temporal streams alongside a parallel DNN stream.Source: §3 · p. 7, Figure 1 · p. 7
3.1 DATAETL Layer
- The DATAETL layer uses trading-day data, past-only moving windows, and training-fitted normalization to prevent temporal leakage.The study uses raw closing prices and a 20-day window, with the first 3,388 trading days for training and the final 365 for held-out testing; test-period model parameters remain frozen.Source: §3.1 · pp. 8–10
3.2 FeatExt Layer
- FeatExt supplies three complementary temporal representations: LSTM sequential memory, Bi-LSTM bidirectional context, and St-LSTM progressive multi-scale abstraction.Each branch produces a 64-dimensional penultimate representation for fusion; the Bi-LSTM’s reverse pass uses only observations within the past lookback window.Source: §3.2 · pp. 10, 12, 13, 14
3.3 VertiFuse Layer
- VertiFuse learns feature-level interactions by vertically fusing temporal branches’ penultimate representations with aligned DNN features before prediction.The model optimizes its temporal and non-temporal mappings and fusion layers jointly through backpropagation.Source: §3.3 · pp. 15–16
3.3.1 Theoretical Motivation for Penultimate-Layer Vertical Fusion.
- Learned feature-level reweighting lets gradients jointly shape the temporal branches and conditionally emphasize different representations without retraining.The method contrasts with decision-level averaging and describes emphasizing Bi-LSTM features in noisy periods and St-LSTM features in stable trends.Source: §3.3.1 · p. 17
3.3 VertiFuse Layer
- Penultimate-layer fusion retains richer temporal representations than compressed predictions, combining features after temporal abstraction but before task-specific regression.The design is intended to avoid both early fusion of raw, noisy features and late fusion of compressed outputs.Source: §3.3 · p. 16, §3.3.1 · p. 17
3.3.2 Information-Preservation Rationale for Penultimate-Layer Fusion.
- Penultimate features carry at least as much target information as their deterministic final outputs, but this representational advantage does not guarantee finite-sample superiority.The paper reports that an ablation found penultimate fusion improved over final-layer fusion under fixed regularisation and comparable fusion-stage parameter count. It does not claim lower variance from reweighting; it notes consistency with larger relative gains over decision-level averaging on volatile NASDAQ and shallower stress-period drawdowns.Source: §3.3.2 · pp. 17–18
3.3.3 Stage 1: Temporal VertiFuse.
- Temporal VertiFuse concatenates LSTM, Bi-LSTM, and St-LSTM penultimate features, then learns an affine, nonlinear reweighting jointly with the branches.The transformation allows branch-specific temporal patterns to be reweighted while mitigating redundancy and multicollinearity.Source: §3.3.3 · p. 18
3.3.4 Stage 2: Joint Temporal–DNN Fusion.
- A parallel DNN processes the lagged window through 128- and 64-unit hidden layers with dropout (p=0.3), then its features are aligned and fused with temporal features.The DNN captures non-recurrent relationships and can integrate static or lower-frequency auxiliary features; the output projection can expand to support direct multi-step forecasting without changing upstream fusion.Source: §3.3.4 · pp. 18–20
4 Experimental results
The experimental results assess VertiFuseX’s forecasting accuracy against state-of-the-art models and baselines, alongside saliency, formal tests and multi-seed results, fusion ablations, economic performance across markets, and computational cost.
4.1 Comparison with Baseline Models
- VertiFuseX achieved the lowest error in all 12 baseline index–metric pairs, with gains up to 54.3% on S&P 500 MAPE and approximately 50% average error reduction versus ARIMA.Baseline comparisons covered LSTM, Bi-LSTM, St-LSTM, and standalone ARIMA on four U.S. indices.Source: §4.1 · pp. 21–22, Table 6 · p. 23
- Learned penultimate-layer fusion reweights LSTM, Bi-LSTM, and St-LSTM representations, shifting temporal sensitivity by market regime without explicit regime detection or hyperparameter changes.The analysis attributes improved forecasts to combining multi-scale features while suppressing high-variance recent-lag features.Source: §4.1 · pp. 24, 26
- Saliency attribution was strongest around lags 9–15 overall, with index-specific peaks ranging from lags 9–11 for NYSE to 14–16 for DJI.Very recent lags (t>17) and very old lags (t<3) received lower attribution; the mid-range pattern emerged from data-driven learning.Source: §4.1 · pp. 24, 26, Figure 8 · p. 26
4.2 Comparison of VertiFuseX with state-of-the-art models
- State-of-the-art comparisons retrained VertiFuseX on the same index and duration as each prior study, spanning ten global indices and varied market regimes.The evaluation includes crisis, recovery, and bull-market periods across North America, Europe, and Asia.Source: §4.2 · p. 27
- The Diebold–Mariano tests found VertiFuseX statistically superior to St-LSTM across all four indices, and three-seed results remained below strongest single-branch baseline errors.The multi-seed analysis used seeds 42, 101, and 150; even the upper bounds of the reported 95% confidence intervals stayed below those errors.Source: §4.2 · pp. 27–28, Table 7 · p. 28, Table 8 · p. 28
- VertiFuseX attained the lowest error across all 33 state-of-the-art metric–dataset combinations, spanning ten indices and diverse markets and timeframes.The comparison aligns VertiFuseX’s training and testing periods with those of prior studies.Source: §4.2 · pp. 27, 30, Figure 9 · p. 29
- 29.36% lower RMSE (28.29 vs. 40.05) against GA-CNN-LSTM on KOSPI illustrates VertiFuseX’s gains in a volatile Asian market.The KOSPI comparison covers 14/09/2014–31/10/2022; across all state-of-the-art comparisons, VertiFuseX had the lowest error in each reported metric–dataset combination.Source: §4.2 · p. 30
4.3 Computational Cost Analysis
- With 675,716 parameters and approximately 2.58 MB memory, VertiFuseX runs inference in 1.47–1.56 ms per sample and achieves up to 34.6% lower MAE.Training across four indices took 100.23–107.55 seconds; inference timing used a warm-up pass followed by 100 forward passes on batches of 64.Source: §4.3 · pp. 30, 32
- VertiFuseX achieves the lowest error in all comparable state-of-the-art cases, with reported improvements over best-reported results.Table 9 presents the unified comparison across stock-index datasets; the supplied passage does not specify the individual metric values.Source: §4.3 · p. 31, Table 9 · p. 31
4.4 Algorithmic Trading Strategy and Economic Evaluation
- Sharpe ratios are 1.43 vs. 1.37 on S&P 500 and 1.15 vs. 1.06 on DJI, despite VertiFuseX returns being near buy-and-hold.VertiFuseX returns 29.41% vs. 29.44% on S&P 500 and 21.44% vs. 21.08% on DJI, while holding approximately 25% cash on average.Source: §4.4 · p. 34, Table 11 · p. 34
- On NASDAQ, VertiFuseX lowers maximum drawdown from -13.15% to -11.97% while trailing buy-and-hold returns; on NYSE, it underperforms buy-and-hold.NYSE is the weakest case: returns are 7.68% vs. 17.31%, and the summary cautions that VertiFuseX does not uniformly dominate passive investment.Source: §4.4 · pp. 34, 36, Table 11 · p. 34
4.5 Ablation Studies
- VertiFuseX reduces MAE versus Final-Layer fusion by 24.2% on S&P 500 and 21.1% on NASDAQ, and MAPE by 36.6% and 37.1%.Because the fusion variants have comparable combination-stage parameter counts, the results point to fusion location, rather than added capacity, as the more likely source of gains.Source: §4.5 · pp. 36–37, Table 12 · p. 36
5 Discussion
VertiFuseX shows improved trading outcomes in the COVID-19 crash and 2022 bear market under the reported stress-test setup. The discussion also identifies limits in its input scope, validation, and trading simulation.
5.1 Robustness Analysis Under Extreme Market Regimes.
- Stress tests froze parameters after training through 27 December 2019 and evaluated through 2024, using a training-distribution 75th-percentile entry threshold.The authors attribute cross-regime drawdown and risk-adjusted improvements to reduced exposure during volatility, controlled re-entry, and cool-down risk controls.Source: §5.1 · p. 37, §5.1.2 · p. 38, Figure 13 · p. 38
5.1.1 COVID-19 Crash (19 February – 30 April 2020).
- VertiFuseX limited maximum drawdown to -26.45% versus Buy & Hold’s -33.67% and returned -9.63%, outperforming Buy & Hold by 6.45 percentage points during COVID-19.Its Sharpe ratio was -0.56 (-0.98 for Buy & Hold; -2.21 for Naive Momentum), with volatility of 61.33% versus Buy & Hold’s 68.13%.Source: Table 13 · p. 37, §5.1 · p. 37, Figure 13 · p. 38
5.1.2 2022 Bear Market (1 January – 31 October 2022).
- During the 2022 bear market, VertiFuseX returned -10.04%, outperforming Buy & Hold by 9.52 percentage points, with maximum drawdown of -17.67% versus -25.38%.Its Sharpe ratio was -0.51 (-1.04 for Buy & Hold; -2.41 for Naive Momentum); volatility was 23.45% versus Buy & Hold’s 24.33%.Source: §5.1.2 · p. 38, Figure 14 · p. 38
5.2 Limitations
- The evaluation uses only closing prices, so forecasts may degrade during exogenous shocks absent from prior price history.The model does not explicitly incorporate macroeconomic indicators, cross-asset correlations, or market microstructure features.Source: §5.2 · p. 39
- Uniform fixed hyperparameters trade market-specific peak accuracy for broader robustness, and one held-out test period leaves rolling walk-forward evaluation outside scope.The study also does not report aggregated statistics across repeated regime transitions or formal cross-regime statistical comparisons.Source: §5.2 · p. 39
- Deterministic point forecasts lack prediction intervals or calibrated uncertainty, limiting their suitability for applications requiring formal confidence bounds.Source: §5.2 · p. 39
- The trading simulation uses simplified logic and conservative assumptions, making it a proof of concept rather than a fully optimized trading system.The authors identify strategy optimization, portfolio integration, and real-world execution tests as future work.Source: §5.2 · p. 39
6 Conclusion and Future Work
VertiFuseX uses penultimate-layer vertical fusion for financial forecasting and outperforms LSTM-family baselines and seven state-of-the-art models in the reported evaluations. Future work will broaden validation and model scope.
6 Conclusion and Future Work
- VertiFuseX achieves up to 54.3% lower MAPE and over 40% lower MAE and RMSE than LSTM-family baselines, outperforming seven state-of-the-art models across 33 comparisons.Source: §6 · p. 39
- The model has approximately 675k parameters and 1.5 ms/sample inference latency for real-time analytical systems.Source: §6 · p. 40
- Future work targets rolling-origin validation, multivariate inputs, design sensitivity analyses, transfer and multi-horizon forecasting, uncertainty estimates, alternative fusion, and added explainability methods.Proposed inputs include OHLCV variables, technical indicators, macro-financial covariates, and cross-asset data; proposed explainability methods include Integrated Gradients and SHAP.Source: §6 · p. 40