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DSTNet: Dynamic Spectral Trajectory Network for Causal Multi-Horizon Financial Forecasting

Aashish Bohra, Lokendra Vishwakarm

arXiv:2610.09654v1cs.LGq-fin.CPq-fin.ST

TL;DR

Wavelet-based financial forecasters may use bilateral transforms that read beyond the forecast origin or retain only a spectral snapshot. DSTNet builds a causal spectral trajectory and combines it with a temporal branch for direct multi-horizon forecasts. It is below persistence in every reported cell, while the allocation diagnostic does not support an equity-timing advantage.

  • Problem

    Wavelet-based forecasters may use bilateral preprocessing that leaks future information or retain only a single spectral snapshot, discarding the evolution of coefficient magnitudes.

    Source: §I · p. 1

  • Method

    DSTNet combines a causal Dynamic Spectral Trajectory with a temporal branch, factorized scale-temporal attention, learned fusion, and direct horizon-specific forecasts.

    Source: §I · p. 1, §VI · p. 18

  • Results

    DSTNet is below persistence in every reported MAE and MAPE cell, by 0.7 to 0.9 percent at one day and 3.4 to 4.5 percent at ten days.

    Source: §VI · p. 18

  • Takeaways & Limitations

    The downstream allocation diagnostic does not support an equity-timing claim on the evaluated indices.

    Source: §VI · p. 18

    Overlapping input windows and multiplicity remain, and directional accuracy is reported without a Pesaran–Timmermann test or interval.

    Source: J. Limitations and Threats to Validity · p. 18

Abstract

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Wavelet-based financial forecasters typically use the transform only to denoise, or reduce it to a single spectral snapshot at the forecast origin, and the convolution that produces the coefficients is usually bilateral, so it can read past the forecast origin. DSTNet instead retains the recent evolution of filter-bank magnitudes as a causal Dynamic Spectral Trajectory, built from seven trailing technical indicators over a twenty-day lookback with a one-sided Morlet-derived filter bank and an explicit burn-in for the left-boundary transient. A factorized Scale-Temporal Spectral Transformer attends along the time and filter-bank axes separately, a learned gate fuses the spectral branch with a CNN-BiLSTM, and horizon-specific gates emit one, three, five, and ten day forecasts in a single pass. We evaluate seven equity indices and gold under a common expanding-window protocol and an untouched one-year hold-out, against nine learned baselines and a random-walk persistence benchmark. Under MAE and MAPE, persistence is the strongest of the ten fixed competitors in 29 of the 32 series-horizon cells and DSTNet is the only model below it in every cell, by 0.7 to 0.9 percent at one day and 3.4 to 4.5 percent at ten days. At one day, paired testing favours DSTNet against the weaker learned baselines but is inconclusive against persistence and the strongest learned forecasters. A downstream allocation diagnostic does not support an equity-timing advantage on any of the seven indices.

I. INTRODUCTION

DSTNet addresses two gaps in wavelet-based forecasting: bilateral preprocessing can leak future information, while static snapshots discard the evolution of spectral structure. It combines a causal spectral trajectory with a dual-branch, multi-horizon forecasting architecture.

I. INTRODUCTION

  • Wavelet hybrids may use bilateral transforms that leak future information or retain only a static spectral snapshot; DSTNet proposes a causal trajectory representation and architecture addressing both gaps.The introduction distinguishes a spectral state at the forecast origin from the path that produced it.Source: §I · p. 1

A. Time-Frequency and Wavelet Methods in Financial Forecasting

  • Prior wavelet-finance work often uses transforms only for denoising, while the reviewed literature leaves causal construction at the forecast origin unaddressed.The authors do not estimate the resulting bias in prior work, which would require rerunning those methods with causal transforms.Source: A. Time-Frequency and Wavelet Methods… · p. 2

B. Decomposition-Based Hybrids for Equities

  • Reviewed decomposition hybrids generally decompose raw prices, aggregate per-scale streams, and use fixed recombination, without a causal spectral trajectory or leakage guarantee.The surveyed methods vary in their decompositions and forecasting networks, but share these stated limitations.Source: B. Decomposition-Based Hybrids for… · p. 2

C. Hybrid Deep Architectures for Equity Index Forecasting

  • DSTNet’s learned vertical gate reweights temporal and spectral branches, extending hybrid forecasting with a causal spectral trajectory and factorized scale-temporal attention.The reviewed hybrid architectures typically combine blocks statically, whereas DSTNet learns sample-dependent branch weights.Source: C. Hybrid Deep Architectures for… · pp. 2–3

D. Multi-Horizon and Trading-Oriented Forecasting in Finance

  • DSTNet’s Horizon-Adaptive Decoder applies an independent learned feature-modulation gate before each horizon head, producing direct multi-step outputs.The cited finance studies generally use shared decoders or conventional per-horizon heads.Source: D. Multi-Horizon and Trading-Oriented… · p. 3

E. Feature Comparison

  • The comparison identifies no listed model combining spectral processing on technical indicators, an explicit causal guarantee, learned fusion, and direct multi-horizon forecasting under one objective.The comparison’s non-equity column describes evaluation scope, not a methodological contribution.Source: E. Feature Comparison · p. 3

III. METHODOLOGY

  • The model denoises OHLCV, builds a causal filter-bank representation, lifts it into a Dynamic Spectral Trajectory, and routes temporal and spectral streams through learned fusion to four forecast horizons.The target is a cumulative log return; price-level metrics are computed after reconstruction to the price scale.Source: §III · p. 3

A. Data and Preprocessing

  • Causal Symlet-4 residual denoising uses thresholds estimated on training data, while training-split normalization and fixed preprocessing constants help restrict processing to information available at the forecast origin.The denoising filters use left padding only, and thresholds are refitted within walk-forward folds before the final hold-out transform.Source: A. Data and Preprocessing · pp. 3–5

B. Causal Morlet-Derived Complex FIR Filter Bank

DSTNet constructs causal Morlet-derived FIR coefficients using only present and past observations, then retains their magnitudes across the lookback as a Dynamic Spectral Trajectory. The filter bank is a fixed feature extractor, not an exact or conventional CWT representation.

B. Causal Morlet-Derived Complex FIR Filter Bank

  • The causal Morlet-derived FIR bank uses nonnegative lags, so each complex coefficient depends only on observations available at or before its time index.The implementation uses zero prehistory for negative indices; the one-sided truncation breaks the conventional Morlet zero-mean admissibility condition.Source: B. Causal Morlet-Derived Complex FIR… · p. 5
  • The eight channels are not a clean daily-to-monthly pseudo-frequency ladder, and results are interpreted for this fixed implemented bank rather than conventional Morlet bands.The nominal carrier at scale 1 folds past the Nyquist limit, and one-sided truncation further changes the response.Source: B. Causal Morlet-Derived Complex FIR… · p. 5

C. Dynamic Spectral Trajectory (DST) Tensor

  • DST stacks filter-bank magnitudes across the lookback, scales, and indicators, retaining spectral evolution instead of only the prediction-time slice.Each sequence has shape (20, 8, 7); the sequence builder enforces the 192-sample burn-in so retained coefficients avoid left-boundary zero-padding contamination.Source: C. Dynamic Spectral Trajectory (DST)… · p. 6

D. Temporal Branch (CNN-BiLSTM)

The architecture pairs a temporal CNN-BiLSTM branch with a factorized spectral transformer that models time and scale separately. Its spectral streams are integrated through a cross-stream projection, trading joint time-scale attention for a restricted interaction structure.

D. Temporal Branch (CNN-BiLSTM)

  • A convolution and two bidirectional LSTM layers summarize the observed 20-day window; the backward traversal remains within that window and does not read beyond the forecast origin.The branch uses no pooling between convolution and recurrence, so the recurrent stack receives all daily positions.Source: D. Temporal Branch (CNN-BiLSTM) · p. 6

E. Spectral Branch: Factorized STST

1) Stream A (temporal-spectral):

  • Stream A reshapes the trajectory into time tokens, each representing the full spectral state at one time step.It uses stacked multi-head self-attention blocks and a learned attention pool.Source: 1) Stream A (temporal-spectral) · p. 6

2) Stream B (scale-spectral):

  • Stream B reshapes the trajectory into scale tokens, each representing the full temporal trajectory at one filter-bank scale.It uses stacked multi-head self-attention blocks and a learned attention pool.Source: 2) Stream B (scale-spectral) · p. 6

3) Cross-stream integration:

  • The two stream outputs are concatenated and projected into a spectral summary, but neither stream forms pairwise scores between time-scale pairs.The factorization therefore restricts direct cross-time, cross-scale interactions; the joint-STST ablation evaluates the trade-off on the authors’ datasets.Source: 3) Cross-stream integration · p. 6, Figure 4 · p. 7

F. Vertical Attention Fusion (VAF)

Vertical Attention Fusion combines temporal and spectral summaries through a learned two-token gate. The gate is shared across forecast horizons.

F. Vertical Attention Fusion (VAF)

  • The temporal and spectral summaries occupy the same fusion space and are stacked as a two-token sequence for learned attention-based fusion.A shared linear scorer produces the two scores used to weight the branch summaries.Source: F. Vertical Attention Fusion (VAF) · p. 7
  • The fused representation is formed from the two branch summaries using normalized attention weights; the shared scalar bias cancels under the two-token softmax.The weights therefore depend on the learned scorer’s weight vector.Source: F. Vertical Attention Fusion (VAF) · p. 7
  • VAF uses one gate across horizons, so horizon-specific branch reliance is not identifiable from this fusion stage.The paper raises a separate gate per horizon as an architectural question for the decoder.Source: F. Vertical Attention Fusion (VAF) · p. 7

G. Horizon-Adaptive Decoder (HAD)

HAD applies independent horizon-specific gates to a fused representation, while the theoretical account establishes causal filtering and a left-boundary burn-in. Factorized attention reduces the quadratic attention core but gives up some joint time–scale interactions.

G. Horizon-Adaptive Decoder (HAD)

  • Each horizon independently gates the fused vector before a scalar head predicts its cumulative log return, and all heads train jointly under one Huber loss.The per-horizon head uses a 32-unit ReLU layer with dropout before its scalar output.Source: G. Horizon-Adaptive Decoder (HAD) · pp. 7–8

1) Scope of the decoder:

  • Because HAD gates only the post-fusion vector, it cannot reweight temporal versus spectral branches separately, leaving horizon-specific branch reliance unidentifiable.The gate performs elementwise modulation inside the fused feature space rather than projecting between branches.Source: 1) Scope of the decoder · p. 8

IV. THEORETICAL FOUNDATIONS

  • The Morlet-derived FIR coefficient and its magnitude at time t depend only on observations at or before t, so the filter bank is causal.The proof follows from the filter’s finite support over indices no later than t.Source: §IV · p. 8
  • 192 samples are required for the largest scale’s FIR taps to be supported entirely by observed history, setting the bank’s left-boundary burn-in.For the scale set ending at 32, the burn-in is B = floor(6 × 32) = 192.Source: §IV · p. 8
  • At configured widths and layer counts, the factorized design’s quadratic attention core is approximately 14.8 times smaller than the joint design’s, before other model costs.The equal-width per-layer ratio of 55.2 is for the quadratic attention core, not total FLOPs or runtime.Source: §IV · p. 8
  • Separate temporal and scale attention streams do not form joint time–scale scores, and pooling can irreversibly discard information before cross-stream mixing.The factorized path is therefore a restricted hypothesis class, not an equivalent design; its empirical trade-off is evaluated with the joint-STST ablation.Source: §IV · p. 9

V. EXPERIMENTS

The experiments use a common chronological protocol across seven equity indices and gold, with the gold series reserved as a non-equity probe. The configuration is selected on equity development folds and then frozen for all eight series.

V. EXPERIMENTS

  • The evaluation reports forecasting accuracy, seed stability, a gold probe, regime diagnostics, ablations, and a downstream allocation diagnostic.The test period is a one-year hold-out from 2023-06-01 to 2024-05-31.Source: §V · p. 9, 1) Data · p. 9

1) Data:

  • Seven equity indices and gold are evaluated with a 20-trading-day lookback and 1-, 3-, 5-, and 10-day horizons under the same protocol.Gold is the single non-equity robustness probe; model selection and threshold calibration use five expanding-window folds before the hold-out.Source: 1) Data · p. 9

2) Hardware and software:

  • The implementation uses deterministic settings, and the main-text tables use seed 42, with a three-seed rerun reported separately.Experiments ran on one workstation with an NVIDIA RTX 5060 Ti GPU.Source: 2) Hardware and software · p. 9

3) Hyperparameters:

  • The development configuration was selected by aggregating validation performance across seven equity-index folds, without using gold validation or test observations, then frozen for all series.Each series retains its own exchange calendar, and missing days are not imputed.Source: 3) Hyperparameters · p. 9, 1) Data · p. 9

B. Targets, Metrics, and Confidence Intervals

The evaluation targets cumulative log returns but computes price-level errors on reconstructed prices, using zero-return persistence as its reference. It applies block-bootstrap intervals and one-day Diebold–Mariano comparisons, with learned baselines retrained under a shared chronological protocol.

B. Targets, Metrics, and Confidence Intervals

  • Targets are cumulative log returns for each horizon, while price-level metrics use reconstructed prices and persistence predicts zero return.The persistence forecast is equivalent to carrying the forecast-origin price forward.Source: B. Targets, Metrics, and Confidence… · p. 9

1) Block-bootstrap confidence intervals:

  • At the 10-day horizon, adjacent forecast errors overlap heavily, leaving only about two dozen disjoint target blocks and warranting cautious interpretation of point estimates.The reported 95% confidence intervals use a moving-block bootstrap with block length 20 and 1,000 resamples per metric.Source: 1) Block-bootstrap confidence intervals · p. 10

2) Diebold–Mariano comparison:

  • One-day Diebold–Mariano tests compare absolute reconstructed-price errors; non-significance means insufficient evidence of unequal expected loss, not proof of equivalence.The nine baseline comparisons per series use unadjusted p-values, making them exploratory rather than familywise-confirmatory.Source: 2) Diebold–Mariano comparison · p. 10

C. Baselines

  • All learned baselines are retrained with the same expanding-window validation folds and final hold-out, while non-reproducible finance-specific methods are excluded from controlled numerical comparisons.The shared pipeline is intended to avoid comparisons assembled from results in source papers with differing protocols.Source: C. Baselines · p. 10

1) Uniform-protocol baselines:

  • The baseline panel contains nine learned models spanning recurrent, tree, attention, and modern forecasting architectures, all using the same denoised history and trailing indicators as DSTNet.DSTNet additionally uses its proposed causal spectral representation, so the comparison tests representation and architecture under a shared information set.Source: 1) Uniform-protocol baselines · pp. 10–11
  • Table IV reports panel-mean error relative to persistence across 32 series–horizon cells for seed 42, with positive values marking worse error and wins shown in parentheses.The reference is the minimum across all ten fixed competitors for each cell.Source: Table IV · p. 11

2) Baseline fairness and random-walk reference:

Under the shared validation protocol, persistence is the binding competitor under MAE and MAPE, while DSTNet is below it in every series-horizon cell. Seed variation qualifies the primary-run results, and the gold probe tests the equity-selected configuration on one non-equity series.

2) Baseline fairness and random-walk reference:

  • All nine learned baselines used the same validation protocol, search methods, trial budgets, criteria, and selection folds as DSTNet, with configurations frozen before hold-out evaluation.Persistence is the zero-return forecast, equivalent to a driftless random walk on reconstructed price levels.Source: 2) Baseline fairness and random-walk… · p. 11

1) Under MAE and MAPE the learned baselines do not improve on the random walk:

  • 2.27% below persistence on panel-mean MAE and MAPE, DSTNet is the only model below persistence in all 32 cells under both metrics.Its MAE margin grows from 0.67–0.92% at H=1 to 3.43–4.49% at H=10; persistence is the lowest non-DSTNet estimate in 29 cells.Source: 1) Under MAE and MAPE the learned… · p. 11
  • At H=1, paired tests favor DSTNet most clearly over LSTM, BiLSTM, and XGBoost, but do not reject equal predictive accuracy against persistence.Only four of 32 comparisons with DLinear, N-BEATS, PatchTST, and iTransformer reach the unadjusted 10% level.Source: 1) Under MAE and MAPE the learned… · p. 11, Table VI · p. 13
  • Directional accuracy is highest for DSTNet on every series, but KOSPI and NYSE are below chance and the table has no accompanying test.The reported values are descriptive.Source: 1) Under MAE and MAPE the learned… · p. 11

2) Qualitative forecast trajectories:

  • At H=1 forecasts track realised prices closely, while gaps emerge around sharp drawdowns and recoveries at H=5 and H=10.Because each reconstruction is anchored to the observed price at the forecast origin, visual proximity is not evidence of skill.Source: 2) Qualitative forecast trajectories · p. 11, Figure 6 · p. 14

E. Random-Seed Stability

  • Across three seeds, median cellwise CV is below 1% for all metrics, but maximum CV reaches 9.69–10.60% and variability concentrates in KOSPI and longer-horizon NASDAQ and NYSE cells.Seed-mean wins fall to 26/32 for MAE and MAPE and 25/32 for RMSE; the 32/32 seed-42 result is not seed-invariant.Source: E. Random-Seed Stability · p. 13

F. Non-Equity Robustness Probe on Gold

  • On gold, trained with its own history and the equity-selected configuration unchanged, DSTNet clears persistence at all four horizons, by 0.67% at H=1 and 4.09% at H=10.This is a fixed-design probe on one non-equity series, not zero-shot transfer or cross-asset generalisation; longer-horizon forecasts visibly lag sharp moves.Source: F. Non-Equity Robustness Probe on Gold · pp. 13–14

G. Regime-Aware and Bias-Aware Diagnostics

The diagnostics show strong volatility-regime and directional asymmetries, but near-zero equity discrimination after bias adjustment. Ablations favor retaining the spectral trajectory, while the allocation diagnostic finds no equity Sharpe improvement over buy-and-hold.

G. Regime-Aware and Bias-Aware Diagnostics

  • High-volatility regimes have larger MAPE on every series; calibrated S&P 500 diagnostics are 98.13% on down days versus 2.22% on up days, yet J is +0.35 percentage points.The passage interprets the asymmetry as a nearly constant negative-sign forecast, not as separation of up and down days.Source: G. Regime-Aware and Bias-Aware… · p. 15, Table VIII · p. 16

H. Ablation Studies

  • 5.79% panel-mean MAE increase makes No-DST the largest ablation degradation, worse on all eight series at both reported horizons despite overlapping bootstrap intervals.Joint STST shifts panel-mean MAE by 0.05%; removing burn-in exclusion and replacing learned fusion with a mean degrade it by 0.92% and 2.94%, respectively.Source: H. Ablation Studies · p. 15, Table IX · p. 16

1) Centred HAD gate variation:

  • Horizon-gate variation spans one to four directions per horizon and mean adjacent angles of 76.89° to 84.58°, but these descriptive statistics do not establish purposeful specialization.The analysis centers gate vectors over the test split, then uses SVD and principal angles; compact rank can also reflect correlated inputs, tanh saturation, or limited sample variation.Source: 1) Centred HAD gate variation · p. 16

I. Downstream Allocation Diagnostic: A Negative Result on Equities

  • Six equity indices retain a static 65% position; NYSE alone changes exposure, but its Sharpe falls from 2.02 to 1.80 as drawdown drops from 10.66% to 5.65%.Gold long-only Sharpe is 1.99 versus 1.74 for buy-and-hold and 1.71 for volatility-targeted buy-and-hold; these one-series, one-hold-out results do not establish an allocation advantage.Source: §I · pp. 16–17

J. Limitations and Threats to Validity

DSTNet’s forecasting advantage is qualified by limits in hold-out size, inference, and component isolation; its allocation diagnostic does not establish an equity-timing advantage. The conclusion reports lower MAE and MAPE than persistence across all series-horizon cells, but the one-day paired test is inconclusive.

J. Limitations and Threats to Validity

  • One hold-out year provides only about two dozen disjoint ten-day target blocks, limiting market-regime coverage; overlapping marginal intervals do not establish equivalence.The moving-block bootstrap preserves local dependence but cannot create additional regimes.Source: J. Limitations and Threats to Validity · p. 17
  • Three seeds rerun only DSTNet, so the seed analysis compares its initialization sensitivity with fixed baseline references rather than seed-matched model differences.Source: J. Limitations and Threats to Validity · p. 17
  • Paired inference covers only the one-day horizon, where persistence is not rejected; the larger three-, five-, and ten-day improvements remain descriptive.The one-day tests use a lag-zero variance estimator and unadjusted p-values, leaving residual dependence from overlapping input windows and multiplicity concerns.Source: J. Limitations and Threats to Validity · pp. 17–18
  • Persistence is strongest under MAE and MAPE, but this comparison does not hold under squared loss at long horizons.Source: J. Limitations and Threats to Validity · p. 18
  • The study does not isolate the denoiser or horizon-adaptive decoder, so its gains support the full pipeline and directly tested components, not either component alone.Branch reliance by horizon is also unidentifiable because vertical attention fusion mixes the branches before horizon-adaptive decoding.Source: J. Limitations and Threats to Validity · p. 18
  • The fixed panel includes seven equity indices and one non-equity series, while the allocation test uses one hold-out, simplified costs, and idealized execution; these results do not establish cross-asset generalization or a general trading advantage.The gold futures proxy also abstracts from contract rolls, margin, roll yield, market impact, and capacity.Source: J. Limitations and Threats to Validity · p. 18

VI. CONCLUSION

  • DSTNet is below persistence in every series-horizon cell under MAE and MAPE, by 0.7–0.9% at one day and 3.4–4.5% at ten days, but the one-day paired test is inconclusive.The three-seed rerun leaves DSTNet ahead of the strongest fixed competitor in 25 or 26 of 32 cells, and the random-walk comparison does not extend to long-horizon RMSE.Source: §VI · p. 18
  • The allocation diagnostic does not support an equity-timing claim: the rule holds a static scaled position on six of seven indices, while the gold improvement rests on one hold-out without paired inference.The static equity position follows removal of validation bias, after which the directional signal retains little conditional discrimination.Source: §VI · p. 18

APPENDIX A ALGORITHMS

Appendix A collects the algorithms needed to reproduce DSTNet, with notation aligned to the main text and output shapes reported after major steps. Appendix B supplies companion metric tables and secondary diagnostics.

APPENDIX A ALGORITHMS

  • Seven algorithms, together with the main-text equations, are collected to support reproduction of DSTNet without the codebase.Notation matches the main text, and output shapes are stated after major steps.Source: Appendix A · p. 20

APPENDIX B FULL METRIC TABLES AND SECONDARY DIAGNOSTICS

  • Appendix B provides RMSE and MAPE companions to Table V, plus directional accuracy, HAD gate-variation statistics, and allocation growth curves.Source: Appendix B · p. 20
  • The allocation growth curves in Fig. 8 are discussed alongside the allocation analysis in Section V-I.Source: Appendix B · p. 20

APPENDIX C RANDOM-SEED STABILITY: CELLWISE RESULTS

The appendix reports cellwise DSTNet results across three random seeds on the primary hold-out. These results underpin the coefficient-of-variation and win-count summaries.

APPENDIX C RANDOM-SEED STABILITY: CELLWISE RESULTS

  • Tables XV–XVII report three-seed means and sample standard deviations for every series–horizon cell; these values underlie the coefficient-of-variation and win-count summaries in Table VII.Source: Appendix C · p. 20
  • The seed tables cover cellwise values rather than only aggregate metrics.Source: Appendix C · p. 20
  • The reported cellwise values underlie the coefficient-of-variation and win-count summaries in Table VII.Source: Appendix C · p. 20

APPENDIX D ABLATION APPENDIX: FULL PANEL SUMMARY

The appendix reports a full-panel ablation summary, companion metrics, and algorithmic details for the forecasting and allocation pipelines. Removing the DST tensor has a horizon-dependent point-estimate penalty in the same direction across the panel, without establishing significant per-series effects.

APPENDIX D ABLATION APPENDIX: FULL PANEL SUMMARY

  • Removing the DST tensor has a horizon-dependent MAE point-estimate penalty in the same direction across all eight series, but this does not establish a significant effect for each series.Table XVIII summarizes macro-averaged degradation; Table XIX supplies MAE at H = 1 and H = 10 for six indices not shown in the main text.Source: Appendix D · p. 20, Table XVIII · p. 27, Table XIX · p. 27
  • The appendix provides full-panel per-horizon RMSE and MAPE tables, directional accuracy at H = 1, and centred HAD gate-variation statistics.The RMSE and MAPE tables report 95% moving-block bootstrap intervals; bold lowest point estimates are descriptive, not claims of significance.Source: Table XI · p. 21, Table XII · p. 22, Table XIII · p. 24
  • Preprocessing applies left-padded causal filtering, residual denoising, and seven trailing-window technical indicators standardized using training-split statistics.Source: Appendix D · p. 23
  • The spectral branch builds causal Morlet-derived filter-bank magnitudes over eight scales and excludes a 192-sample burn-in for the left-boundary transient.Source: Appendix D · p. 23
  • Sequence construction pairs a 20-step temporal window and spectral trajectory with targets at horizons one, three, five, and ten days, ending inputs at the forecast origin.Source: Appendix D · p. 23
  • The factorized spectral transformer attends separately across time and scales, pools each stream, then uses an MLP to fuse them.Source: Appendix D · p. 24
  • Vertical attention fuses the temporal and spectral branches, and a horizon-adaptive decoder modulates the fused features to emit four forecasts.Source: Appendix D · p. 24
  • The allocation appendix specifies validation-calibrated exposure rules and reports growth curves for S&P 500 and gold at 10 bps.The S&P 500 risk-off rule behaves as static 65% exposure after its initial allocation; gold has higher Sharpe but lower cumulative return than buy-and-hold.Source: Appendix D · p. 25, Figure 8 · p. 26
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