WaVeFuse: Regime-Adaptive Equity Index Forecasting via Channel-Wise Wavelet Denoising and Vertical Attention Fusion

Aashish Bohra; Vivek Vijay

cs.LGSep 13, 2026

WaVeFuse: Regime-Adaptive Equity Index Forecasting via Channel-Wise Wavelet Denoising and Vertical Attention Fusion

Authors: Aashish Bohra, Vivek Vijay

Organizations: Department of Computer Science and Engineering, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

Abstract

Hybrid Deep Learning for equity index forecasting is limited by three problems: propagation of OHLCV noise into derived technical indicators (TIs), channel-indiscriminate multi-scale decomposition that conflates heterogeneous frequency signatures, and static multi-branch fusion that cannot adapt to market regime shifts. WaVeFuse addresses these limitations through a unified dual-branch architecture. Symlet-4 wavelet denoising (level 2, MAD soft threshold) suppresses microstructure noise in OHLCV. Seven low-lag TIs computed from denoised prices are encoded by a causal channel-wise continuous wavelet transform (Morlet, 32 scales) into a per-timestep scale-space matrix. A CNN-BiLSTM branch captures temporal dynamics, while a dual-layer Transformer (heads=4, dk in {16, 32}) models inter-scale spectral dependencies, and their representations are integrated by a 2-token softmax gate Vertical Attention Fusion (VAF) that dynamically reweights branches as market regimes shift. Evaluated under walk-forward validation (WFV) on KOSPI, DAX, NYSE Composite, and Russell 2000 (2010-2023), WaVeFuse achieves R2 = 0.81-0.96 and directional accuracy 70.5-78.3%. It outperforms seven state-of-the-art models by 8.9-20.2% MAE across twelve dataset-period configurations. Diebold-Mariano statistics (4.62-10.38, p<0.001) confirm superiority over a well-tuned XGBoost benchmark across four indices. Ablation verifies component-wise contributions. Under realistic backtesting with 10 basis point transaction costs, WaVeFuse's directional strategy achieves a mean Sharpe ratio of 3.69 across four markets and limits maximum drawdown to 7.5% during the COVID-19 crash. With 152k parameters (0.68MB) and sub-1.3ms GPU inference, WaVeFuse delivers a computationally efficient, regime-robust framework suitable for research and decision-support deployment.

Figures & tables

Abbrev.	Full Form	Abbrev.	Full Form
Architecture & Models
WaVeFuse	Wavelet-based Vertical Fusion architecture	VAF	Vertical Attention Fusion
CWWT	Channel-Wise Continuous Wavelet Transform	CNN	Convolutional Neural Network
BiLSTM	Bidirectional Long Short-Term Memory	LSTM	Long Short-Term Memory
BiGRU	Bidirectional Gated Recurrent Unit	TCN	Temporal Convolutional Network
DNN	Deep Neural Network	ANN	Artificial Neural Network

Table 1: List of abbreviations used throughout the paper.

Paper	Decomposition Applied to TIs	Channel-Wise Multi-Scale TI Processing	Dynamic Fusion Mechanism	Datasets	Key Innovation	Primary Limitation Relative to WaVeFuse
Rezaei et al. (2021)	No	No	Linear aggregation	4 indices (2010-2019)	CNN feature extraction per IMF	Univariate price, shallow layers, no TI denoising
Ge (2025)	No	No	Linear aggregation	8 indices (2013-2022)	MEMD + Aquila-optimized LSTM	High compute, OHLCV only, static fusion
Yu et al. (2025)	No	No	Linear aggregation	3 indices (2012-2021)	GA-optimized VMD + TCN	Univariate close, no channel-wise TI scales
Gong and Xing (2024)	No	No	Linear aggregation	2 indices high/low (2010-2023)	ICEEMDAN + PSO-VMD re-decomp. + BiLSTM-SAM-TCN	Price-only, static fusion
Li et al. (2026)	Partial (level-1 SWT on derived deviation)	No	None (single-branch)	2 stocks (2010-2023)	SWT preprocessing + multi-layer BiLSTM	Only 2 assets, no channel-wise TI CWT, no fusion
Tian et al. (2025)	No	No	End-to-end joint training	3 indices (2017-2024)	BiLSTM + mod. Transformer + TCN	Univariate close, no explicit dynamic fusion

Table 2: Systematic Comparison of Related Hybrid Forecasting Models

Figure 1: The WaVeFuse Architecture. Left: Preprocessing pipeline with wavelet denoising and sliding-window validation. Center: Dual-branch encoder (CNN-BiLSTM for temporal dynamics; Transformer for spectral-scale dependencies). Right: VAF and prediction decoder.

Figure 2: The Sliding-Window WFV protocol. Each fold (Pass) shifts forward by

s=21

days, ensuring that hyperparameters are tuned on

\mathcal{D}_{\text{val}}

and evaluated on unseen future data, thus maintaining strict temporal causality.

Name of Index	Symbol	Duration	Total Trading Days	Training Data	Test Data
KOSPI	ˆ KS11	01-01-2010 – 31-12-2023	3,448	3,083	365
DAX	ˆ GDAXI	01-01-2010 – 31-12-2023	3,552	3,187	365
NYSE Composite	ˆ NYA	01-01-2010 – 31-12-2023	3,522	3,157	365
Russell 2000	ˆ RUT	01-01-2010 – 31-12-2023	3,522	3,157	365

Table 3: Indices under study along with their duration, total trading days, and partitioned data for training and testing

Indicator	Formula
Relative Strength Index (RSI)	$\displaystyle\text{RSI}=100-\frac{100}{1+\text{RS}},\hskip 9.24994pt\text{where }\text{RS}=\frac{\text{Avg gain over }n\text{ days}}{\text{Avg loss over }n\text{ days}}$
	(We use $n=10$ to reduce lag. gains/losses are smoothed exponentially.)
Stochastic %K (SO%K)	$\displaystyle\text{Stoch\%K}=100\times\frac{C-L_{n}}{H_{n}-L_{n}}$
	where $C$ = current close, $H_{n}$ = highest high over $n=14$ days, $L_{n}$ = lowest low over $n=14$ days.
Commodity Channel Index (CCI)	$\displaystyle\text{CCI}=\frac{P-\text{SMA}(P,n)}{0.015\times\text{MAD}(P,n)}$
	where $P=(H+L+C)/3$ , SMA = simple moving average, MAD = mean absolute deviation, $n=14$ .

Table 4: TI’s used in WaVeFuse and their mathematical definitions.

Figure 3: VAF for Regime-Adaptive Integration

Metric	Mathematical Expression	Purpose and Meaning
Huber Loss	$\mathcal{L}_{\delta}(p,\hat{p})$ = $\begin{cases}\frac{1}{2}(p-\hat{p})^{2}&\text{if }\|p-\hat{p}\|\leq\delta\\ \delta\|p-\hat{p}\|-\frac{1}{2}\delta^{2}&\text{otherwise}\end{cases}$	Robust loss used during training. It combines MSE for small errors and MAE for large errors.
RMSE	$\sqrt{\frac{1}{N}\sum_{t=1}^{N}(\hat{p}_{t}-p_{t})^{2}}$	Root Mean Squared Error on inverse-scaled closing prices. Penalizes large errors.
MAE	$\frac{1}{N}\sum_{t=1}^{N}\|\hat{p}_{t}-p_{t}\|$	Mean Absolute Error on inverse-scaled prices. It measures average prediction deviation.
MAPE	$\frac{100}{N}\sum_{t=1}^{N}\left\|\frac{p_{t}-\hat{p}_{t}}{p_{t}}\right\|$	Mean Absolute Percentage Error. Scale-independent measure of prediction accuracy.
$R^{2}$	$1-\frac{\sum_{t=1}^{N}(p_{t}-\hat{p}_{t})^{2}}{\sum_{t=1}^{N}(p_{t}-\bar{p})^{2}}$	Coefficient of determination, fraction of price variance explained by the model.
Directional Accuracy (DA)	$\frac{1}{T-1}\sum_{t=1}^{T-1}\mathbb{I}\big[(p_{t+1}-p_{t})(\hat{p}_{t+1}-\hat{p}_{t})>0\big]\times 100\%$	Percentage of correctly predicted price movement directions (up/down).

Table 5: Evaluation metrics and loss function used in WaVeFuse.

Category	Parameter	Symbol / Value	Rationale
Data	Input window size	$w=20$ ( SEQ_LENGTH )	Captures short to medium term temporal dynamics
	OHLCV features	$f_{\text{OHLCV}}=5$ ( Open, High, Low, Close, Volume )	Preserves microstructure by avoiding close only bias
	TI channels	$f_{\text{TI}}=7$ ( RSI, Stoch%K, CCI, OBV, ATR, Williams%R, ROC )	Low-lag, momentum focused signals
	Final test set	$N_{\text{test}}=365$ days (last year)	Strict chronological hold-out for out of sample evaluation
	Train/val in WFV	Train $\approx 5$ years, Val $=90$ days, Step $=21$ days	Rolling origin validation mimicking live deployment
Preproc.	Denoising	Sym-4, level $=2$	Removes high frequency noise while preserving trends

Table 6: WaVeFuse initialization, preprocessing, and training settings

Model	KOSPI			DAX			NYSE			Russell 2000
	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE
BiLSTM	15.28	18.84	0.61	219.36	275.03	1.40	194.38	238.15	1.11	37.28	46.14	0.96
CNN	17.62	22.15	0.71	255.30	330.00	1.63	225.43	281.67	1.29	43.47	54.92	1.12
Transformer	13.81	16.73	0.55	199.74	246.78	1.27	176.24	214.58	1.01	33.94	41.28	0.87
WaVeFuse	12.30	14.96	0.49	178.34	217.93	1.14	157.51	192.21	0.90	30.34	37.13	0.78
WaVeFuse vs. BiLSTM:	19.5	20.6	19.7	18.7	20.8	18.6	19.0	19.3	18.9	18.6	19.5	18.8

Table 7: WaVeFuse vs. baseline comparison on four indices (best values bold and % reduction in italics )

Figure 4: Percentage improvement of WaVeFuse over the three single-branch baselines (BiLSTM, CNN, Transformer) across four equity indices. Raw error values of the baselines are shown in parentheses next to each point (lower is better). Higher percentage values indicate better relative performance of WaVeFuse.

Panel of Figure 5 — Figure 5: Actual vs. Predicted closing prices for all four equity indices over the 365-day out-of-sample test period (January–December 2023). WaVeFuse predictions are in red and realized prices in black.

Panel of Figure 6 — Figure 6: Scatter plot with correlation and $R^{2}$ value

Panel of Figure 7 — Figure 7: VAF branch attention weights for a representative test-set prediction across all four indices. The CWWT spectral branch consistently receives higher weight than the OHLC temporal branch, confirming the predictive dominance of multi-scale indicator features

Panel of Figure 8 — Figure 8: Attention Allocation Across Test Samples Under Varying Market Conditions: The model assigns significantly higher attention weights to the CWWT branch (orange) compared to the OHLC branch (blue) across all sampled test instances, suggesting that wavelet-transformed features capture more predictive signal than raw price data during out-of-sample evaluation

Panel of Figure 9 — Figure 9: Prediction Errors Over Time: Residual Dynamics During Out-of-Sample Testing. The residuals (Actual – Predicted) exhibit time-varying behavior suggesting sensitivity to market volatility or structural regime changes

Dataset	Duration	Reference	MAE	RMSE	MAPE
S&P 500	01/01/2016 to 29/06/2021	Ji et al. (2024)	29.02	38.04	0.78
S&P 500	01/01/2016 to 29/06/2021	WaVeFuse	25.03 ( 13.8% $\downarrow$ )	33.43 ( 12.1% $\downarrow$ )	0.650 ( 16.7% $\downarrow$ )
DJI	01/01/2016 to 29/06/2021	Ji et al. (2024)	205.86	271.53	0.68
DJI	01/01/2016 to 29/06/2021	WaVeFuse	174.75 ( 15.1% $\downarrow$ )	232.70 ( 14.3% $\downarrow$ )	0.555 ( 18.4% $\downarrow$ )
IXIC	01/01/2016 to 29/06/2021	Ji et al. (2024)	126.17	165.71	1.00
IXIC	01/01/2016 to 29/06/2021	WaVeFuse	110.27 ( 12.6% $\downarrow$ )	146.15 ( 11.8% $\downarrow$ )	0.850 ( 15.0% $\downarrow$ )

Table 8: Unified comparison of WaVeFuse against multiple state-of-the-art models across diverse stock index and individual stock datasets.

Figure 10: Relative performance improvement (%) of WaVeFuse over seven state-of-the-art models (and their specific index/dataset configurations) on MAE, RMSE, and MAPE. Improvements are computed against the originally reported errors in each reference. Dashed lines indicate missing metrics in the source paper (n/a). Higher bars indicate larger error reductions achieved by WaVeFuse

Index	DM Stat	$p$ -value	Paired $t$	$p$ -value	$R^{2}$	DA (%)
KOSPI	4.62	$<$ 0.001	4.38	$<$ 0.001	0.9640	78.26
DAX	10.38	$<$ 0.001	13.97	$<$ 0.001	0.8098	70.51
NYSE	10.24	$<$ 0.001	14.33	$<$ 0.001	0.8444	75.94
Russell 2000	10.06	$<$ 0.001	14.94	$<$ 0.001	0.8276	71.23

Table 9: Statistical significance of WaVeFuse against XGBoost across four equity indices. DM denotes the Diebold‑Mariano test statistic (squared loss). Paired

t

denotes the one‑sided paired

t

‑statistic on absolute error differentials.

R^{2}

and directional accuracy are reported for WaVeFuse on the held-out test set.

Dataset	Parameters	Training Time (s)	Inference Time (ms/sample)	Model Size (MB)
KOSPI	152,116	101.63	0.95	0.68
GDAXI		99.42	0.98
NYSE Composite		109.36	1.26
Russell 2000		101.11	1.22

Table 10: Computational cost of WaVeFuse across four diverse markets.

	KOSPI			DAX			NYSE			Russell 2000
Variant	MAE	RMSE	MAPE(%)	MAE	RMSE	MAPE(%)	MAE	RMSE	MAPE(%)	MAE	RMSE	MAPE(%)
WaVeFuse_no_wavelet_denoising	14.60	18.23	0.58	212.28	265.81	1.36	187.60	234.11	1.06	35.92	45.08	0.92
WaVeFuse_no_CWWT	13.71	17.07	0.55	198.95	247.64	1.27	176.09	218.35	1.00	33.77	42.26	0.87
WaVeFuse_no_VAF	13.00	15.97	0.52	188.72	231.79	1.21	166.96	205.44	0.95	31.98	39.51	0.82
WaVeFuse_MLP_decoder	12.74	15.51	0.51	184.82	225.89	1.18	163.25	199.04	0.93	31.47	38.59	0.81
WaVeFuse_proposed	12.30	14.96	0.49	178.34	217.93	1.14	157.51	192.21	0.90	30.34	37.13	0.78

Table 11: Ablation study results across four equity indices. Each row removes or replaces one component of WaVeFuse while holding all else fixed. Best results in bold .

\Delta

MAE denotes percentage degradation relative to WaVeFuse_proposed.

Removed Component	KOSPI	DAX	NYSE	Russell	Mean
Wavelet Denoising	+18.7%	+19.0%	+19.1%	+18.4%	+18.8%
CWWT Spectral Encoding	+11.5%	+11.6%	+11.8%	+11.3%	+11.6%
VAF Adaptive Fusion	+5.7%	+5.8%	+6.0%	+5.4%	+5.7%
BiLSTM Decoder (vs. MLP)	+3.6%	+3.6%	+3.6%	+3.7%	+3.6%

Table 12: Average MAE degradation (

\Delta

MAE%) per ablated component, averaged across all four equity indices. Each row quantifies the isolated contribution of the corresponding module to WaVeFuse’s forecasting performance.

Index	Strategy	CAGR	Ann. Vol	Sharpe	95% CI (Sharpe)	Max DD	PF	Win Rate	Final Value (currency units)
KOSPI	$\text{WaVeFuse}_{\text{directional}}$	34.4%	5.9%	4.73	[4.37, 5.09]	1.9%	2.86	63.0%	12,760
	$\text{WaVeFuse}_{\text{risk-adjusted}}$	22.3%	5.1%	3.63	[3.35, 3.91]	1.9%	2.73	61.2%	11,809
	XGBoost Baseline	10.3%	5.9%	1.37	—	5.0%	1.43	46.0%	10,847
	Buy & Hold	4.8%	14.2%	0.19	—	16.3%	—	—	10,478
GDAXI	$\text{WaVeFuse}_{\text{directional}}$	13.3%	5.4%	1.96	[1.78, 2.14]	4.3%	1.62	46.6%	11,138
	$\text{WaVeFuse}_{\text{risk-adjusted}}$	9.7%	4.2%	1.76	[1.60, 1.92]	2.3%	1.90	51.2%	10,837

Table 13: Backtesting performance metrics for WaVeFuse strategies versus XGBoost baseline and Buy & Hold across equity indices. Metrics are computed on daily portfolio returns over the test period.

Panel of Figure 11 — Figure 11: Portfolio value over time for three strategies: In all plots, ‘ $\text{WaVeFuse}_{\text{directional}}$ ‘ and ‘ $\text{WaVeFuse}_{\text{risk-adjusted}}$ ‘ refer to the two strategy variants. The XGBoost baseline serves as a traditional ML benchmark

Metric	$\text{WaVeFuse}_{\text{directional}}$	$\text{WaVeFuse}_{\text{risk-adjusted}}$	XGBoost	Buy & Hold
Average CAGR (%)	24.6	19.0	6.8	7.1
Average Sharpe Ratio	3.69	3.16	0.77	0.33
Average Maximum Drawdown (%)	3.7	2.5	6.1	14.8
Average Win Rate (%)	57.1	56.4	42.6	—
Consistency (Sharpe ¿ 1.5)	4/4	4/4	1/4	0/4
Risk Control (Max DD ¡ 5%)	3/4	4/4	1/4	0/4

Table 14: Performance Comparison of Trading Strategies. Consistency thresholds follow benchmarks: Sharpe ¿1.5 indicates strong risk-adjusted performance Lo (2002) , Max DD ¡5% reflects typical institutional tolerances.

Metric	WaVeFuse (Dir.)	WaVeFuse (Risk-Adj.)	XGBoost	Buy & Hold
COVID-19 Crash (Feb–Apr 2020)
Total Return (%)	-0.39	-6.15	-0.61	-11.89
Annualized Return (%)	-1.97	-27.40	-3.05	-47.16
Sharpe Ratio	-0.12	-2.85	-0.17	-1.09
Maximum Drawdown (%)	-7.50	-6.54	-7.60	-34.05
Volatility (%)	18.97	11.67	19.39	49.03

Table 15: Crisis-Period Performance Decomposition: KOSPI (KS11) Index

Figure 12: Crisis Performance Duality: WaVeFuse architectures deliver superior risk-adjusted returns during (a) the COVID-19 crash and (b) the 2025 tariff war. Bars indicate total return generation, while dashed lines show maximum drawdown magnitude. The model demonstrates an asymmetric advantage: limiting losses during crashes while capturing upside during volatile recoveries

Figure 13: Return-Risk Decomposition: Stacked visualization of absolute return generation versus drawdown control demonstrates WaVeFuse’s asymmetric advantage. (Left) COVID-19 crash: $\text{WaVeFuse}_{\text{directional}}$ achieves 4.5 $\times$ lower drawdown than Buy & Hold (7.5% vs 34.0%) with near-neutral returns (-0.4%). (Right) Trump tariff war (2025): $\text{WaVeFuse}_{\text{risk-adjusted}}$ achieves 10 $\times$ lower drawdown than Buy & Hold (1.3% vs 14.1%) while maintaining positive returns (3.1%). Return bars (blue) and maximum drawdown bars (red) are color-coded by strategy, with numerical labels indicating exact percentages

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