HARN: Hierarchical Associative Resonance Network for Event-Driven Multi-Timeframe Forecasting

Nabeel Ahmad Saidd

cs.LGSep 20, 2026

HARN: Hierarchical Associative Resonance Network for Event-Driven Multi-Timeframe Forecasting

Authors: Nabeel Ahmad Saidd

Organizations: Dr. APJ Abdul Kalam Technical University

Abstract

Financial time series evolve across multiple temporal resolutions, challenging forecasting systems to incorporate newly available information without repeatedly recomputing unchanged representations. We introduce HARN, a Hierarchical Associative Resonance Network for event-driven multi-timeframe forecasting. HARN maintains persistent representations across temporal levels and updates each level only when its corresponding completed bar becomes available. The architecture combines causal multi-scale temporal encoding, gated associative memory, cross-level resonance, and hierarchical evidence aggregation, with forecasting performed in basis-point space and reconstructed to the original price scale. We evaluate HARN on four assets spanning equity, foreign exchange, and commodity markets using multiple random seeds and component ablations. HARN achieves competitive reconstructed-price forecasting errors against single-timeframe PatchTST and TimeXer baselines, while ablations reveal the effects of removing individual components across assets and timeframes. A code-level audit further examines consistency between the implementation and the defined event-driven causal protocol. The results position HARN as a persistent multi-timeframe forecasting framework rather than evidence of universal predictive superiority.

Figures & tables

Figure 1: Overview of HARN’s event-driven computational path at one anchor event: per-level causal encoding, prior-state resonance, gated memory candidates, ordered bottom-up evidence, posterior resonance, and per-level forecasting. Conceptual schematic, not an empirical result.

Figure 2: Causal multi-scale encoder: left-padded dilated branches, a learned branch mixture, and decayed pooling. Conceptual schematic, not an empirical result.

Figure 3: Gated associative memory cell: key, value, and query projections, the retrieval residual $s_{t}$ , and the bounded gated write of Eq. 17 . Conceptual schematic, not an empirical result.

Figure 4: The two cross-level communication paths of HARN: all-to-all, contemporaneous resonance ( Eq. 22 ) and directional, ordered bottom-up evidence ( Eq. 23 ). Conceptual schematic, not an empirical result.

Figure 5: Event-driven multi-timeframe timeline. The anchor stream generates forecast events; a coarser representation is updated only when its completed-bar timestamp equals the anchor timestamp and is otherwise carried forward. Conceptual schematic of the protocol, not an empirical result.

Asset	Split	Hierarchy	Anchor	Observations	Period	Span (days)	Mean update
AAPL	Train	M15,H1	M15	43,331	2017-02-07 $\to$ 2023-09-27	2,423.1	0.616
AAPL	Val	M15,H1	M15	9,285	2023-09-27 $\to$ 2025-03-06	525.8	0.615
AAPL	Test	M15,H1	M15	9,286	2025-03-06 $\to$ 2026-08-10	522.2	0.615
EURUSD	Train	M15,H1,H4	M15	69,967	2022-07-26 $\to$ 2025-05-15	1,024.2	0.438
EURUSD	Val	M15,H1,H4	M15	14,992	2025-05-15 $\to$ 2025-12-19	218.2	0.438
EURUSD	Test	M15,H1,H4	M15	14,994	2025-12-19 $\to$ 2026-07-29	221.8	0.437

Table 1: Dataset and split statistics as supplied. Each row gives, for one asset and chronological split, the hierarchy, anchor timeframe, number of anchor-event observations, period, span in days, and mean update rate (the event-update rate averaged across levels). Per-level update rates are listed beneath the table.

Dimension	HARN	PatchTST	TimeXer
Scope	Multi-timeframe, event-driven	Single-timeframe, anchor-only	Single-timeframe, anchor-only
Input	5 OHLCV, all payload levels	5 OHLCV, anchor only	5 OHLCV, anchor only
Lookback / horizon	32 per level / 1	32 / 1	32 / 1
Training target	Stationary BPS delta	Normalized absolute-close target	Normalized absolute-close target
Batch/protocol	256 (reported recipe); stateful contiguous streams	256 shuffled; stateless	256 shuffled; stateless
Schedule; patience	Cosine; 15	Constant; 5	Constant; 5

Table 2: Scope and training differences between HARN and the single-timeframe baseline trainers. PatchTST and TimeXer are trained on the anchor timeframe, their native configuration, whereas HARN is evaluated as a multi-timeframe model. These differences make the comparison in Table 4 descriptive: it does not isolate architecture, target definition, or training recipe.

Reported item	Associated configuration	Determined / not determined
Dataset table ( Table 1 )	Supplied dataset table; dataset_config is available in the repository.	Values are transcribed. Raw vendor data cannot be redistributed, but the dataset can be regenerated from a compatible vendor feed with the vendor-neutral preprocessing pipeline.
HARN rows, Panels A and B (mean $\pm$ SD over three seeds)	Supplied recipe: batch size 256, 50 epochs, AdamW ( $10^{-3}$ , $10^{-5}$ ), clipping 1.0, cosine schedule, patience 15, CUDA AMP if available; seeds 42, 151, 359.	The recipe coincides with the production defaults except for the seed list ( Table 8 ). Seed-specific checkpoints and per-seed aggregate metric CSVs are available, and per-event predictions can be generated from them with the preprocessing pipeline. The standalone evaluator uses one stream, whereas the recipe describes eight; the stream count behind the metrics should be read from the available configuration and checkpoint metadata. Whether Panels A and B came from the same checkpoints is documented in repository metadata where available and is otherwise unresolved.
PatchTST and TimeXer rows, Panel A	Baseline configuration of Table 2 : single-timeframe, anchor-only, dimensions and patching as in Section 6 , batch 256 shuffled, constant learning rate, patience 5, no AMP.	Per-seed aggregate metrics are available in the repository, and per-event predictions can be generated from the available pipeline and checkpoints. In Panel A, HARN and the baselines are reported at the anchor timeframe of each asset (M15 for AAPL, EURUSD, and USDCHF; M5 for XAUUSD).
Ablation variants A0–A3 ( Table 5 )	Ablation trainer defaults: batch 256, five epochs, seed 42, cosine schedule, patience 15, with configuration and seed retained in its checkpoint format.	The supplied evidence does not establish that these defaults were used for the table or identify repeated runs. A0 is full HARN within the ablation pipeline, but its values differ from the main HARN means and are not verified replicates; the reason is undetermined ( Section 8 ).
Figures 6 and 7	Supplied evaluation visualizations.	The captions do not identify asset, timeframe, seed, checkpoint, or split; the underlying predictions can be regenerated from the available checkpoints and preprocessing pipeline.
Audit table ( Table 6 )	Static inspection of the source code.	Not an experiment ( Section 9 ).

Table 3: Provenance of each reported item, based on statements in this manuscript and the repository artifacts. For each item, the table gives the associated configuration and what is and is not determined from the current materials.

Panel A: HARN (multi-timeframe) versus single-timeframe anchor-only baselines (descriptive)
Panel/asset	Model/TF	MAE	RMSE	sMAPE	MASE
AAPL	HARN/M15	0.507696 $\pm$ 0.000509	0.933489 $\pm$ 0.000420	0.204947 $\pm$ 0.000209	1.327584 $\pm$ 0.001331
	PatchTST/M15	2.074401 $\pm$ 0.575730	2.702157 $\pm$ 0.559581	0.794647 $\pm$ 0.219045	5.424392 $\pm$ 1.505489
	TimeXer/M15	2.881886 $\pm$ 0.811630	3.613453 $\pm$ 0.848218	1.115299 $\pm$ 0.292503	7.535901 $\pm$ 2.122348
EURUSD	HARN/M15	0.000306 $\pm$ 0.000002	0.000467 $\pm$ 0.000002	0.026311 $\pm$ 0.000188	0.865688 $\pm$ 0.006210
	PatchTST/M15	0.000759 $\pm$ 0.000275	0.000967 $\pm$ 0.000305	0.065011 $\pm$ 0.023455	2.144210 $\pm$ 0.777650

Table 4: Forecasting results on the test split, reported as mean

\pm

standard deviation across three seeds. Lower is better for every metric, and all metrics are computed on reconstructed absolute price. Panel A is a descriptive, scope-specific comparison between HARN (multi-timeframe, event-driven, BPS target, stateful training) and single-timeframe PatchTST and TimeXer trained on the anchor timeframe; it does not isolate architecture, target definition, or training recipe. Panel B reports HARN at further timeframes, for which no baseline was run; its XAUUSD M5 row repeats the Panel A entry. Values are reproduced as supplied.

Figure 6: Representative forecasts against actual trajectories, taken from the supplied evaluation outputs. The asset, timeframe, seed, and split are not identified in the supplied materials, so the figure gives qualitative context only.

Figure 7: Representative forecast-error distributions across models and assets, taken from the supplied evaluation outputs. The provenance limits are the same as for Figure 6 , and the figure gives qualitative context only.

Asset	TF	Variant	MAE	RMSE	sMAPE	MASE
AAPL	H1	A0	1.055134	1.801484	0.424678	4.799395
AAPL	H1	A1	1.056989	1.798886	0.425441	4.807829
AAPL	H1	A2	1.060339	1.803577	0.426672	4.823069
AAPL	H1	A3	1.058882	1.796596	0.426056	4.816440
AAPL	M15	A0	0.506070	0.932352	0.204299	1.326365
AAPL	M15	A1	0.507230	0.933322	0.204760	1.323333

Table 5: Ablation variants as supplied, for AAPL and EURUSD only. Each cell is a single aggregate value without per-seed uncertainty, and lower is better. A0 is full HARN; A1 replaces the associative memory with a gated recurrent update; A2 replaces resonance with the identity map; A3 zeros the bottom-up evidence readout. Configuration provenance is given in Table 3 .

Figure 8: Relative component degradation $\Delta_{i}$ ( Eq. 28 ) of ablation variants, by asset, timeframe, and variant, derived from Table 5 . The plot summarizes single aggregate values; it is not a statistical test and carries no uncertainty.

#	Dimension	Mechanism observed in the code	Finding
1	Splitting	Chronological 70/15/15 train–validation–test slices	Consistent
2	Alignment	Latest completed timestamp no later than the anchor; exact timestamp equality determines an update	Consistent
3	Windows/ targets	Window ends at the selected completed bar; target is the next completed bar	Consistent
4	Statistics	Training-only feature and target statistics are reused during evaluation	Consistent
5	Local causality	Left-only padding and shifted previous-close features avoid dependence on future observations	Consistent
6	Resonance	Only states available at the same event are mixed	Consistent

Table 6: Condensed code-level causal-consistency audit from a static review of the source code; it is not an empirical causality test. “Consistent (qualified)” denotes consistency with the event-level information-ordering contract, subject to the same-event evidence-ordering qualification of Section 3 .

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Stage	Shape
Raw window $X^{k}$	$B\times T\times 5$
Derived features $d_{t}^{k}$	$B\times T\times 6$
Encoder output $e^{k}$ ( Eq. 12 )	$B\times 72$
Update mask $m_{\tau}^{k}$ ( Eq. 3 )	$B$
Memory input $x_{t}$ (base / higher level)	$B\times 144$ / $B\times 216$
Memory $M_{t}$	$B\times 72\times 18$

Appendix

Table 7: Tensor shapes at each pipeline stage in the default configuration (

d_{s}=72

d_{m}=18

T=32

d_{r}=36

B

is the batch size and

L

the number of configured levels for the asset in question.

Setting	Production	Main results	Ablations
Batch size	256	256	256
Max epochs	50	50	5
Evaluation streams	8	8	8
Optimizer	AdamW	AdamW	AdamW
Learning rate	$10^{-3}$	$10^{-3}$	$10^{-3}$
Weight decay	$10^{-5}$	$10^{-5}$	$10^{-5}$

Appendix

Table 8: Key training settings of the production trainer, the reported main-results recipe, and the ablation trainer. The configurations differ only in the seed lists and in the ablation epoch budget; shared values are shown explicitly rather than inferred.

Asset	TF	Seed	MAE	RMSE	sMAPE	MASE
AAPL	H1	42	$1.058\,752$	$1.801\,058$	$0.425\,964$	$4.815\,850$
		151	$1.060\,329$	$1.800\,236$	$0.426\,467$	$4.823\,021$
		359	$1.058\,117$	$1.799\,379$	$0.425\,760$	$4.812\,961$
	M15	42	$0.506\,980$	$0.933\,028$	$0.204\,653$	$1.325\,713$
		151	$0.507\,987$	$0.933\,396$	$0.205\,064$	$1.328\,345$
		359	$0.508\,120$	$0.934\,044$	$0.205\,123$	$1.328\,694$

Appendix

Table 9: HARN per-seed aggregate test metrics for seeds 42, 151, and 359, grouped by asset and timeframe. The means and standard deviations in Table 4 are computed from these values.

Asset	Model	TF	Seed	MAE	RMSE	sMAPE	MASE
AAPL	PatchTST	M15	42	$1.358\,967$	$1.949\,987$	$0.527\,755$	$3.553\,591$
			151	$2.095\,496$	$2.865\,226$	$0.791\,903$	$5.479\,553$
			359	$2.768\,740$	$3.291\,260$	$1.064\,283$	$7.240\,032$
	TimeXer	M15	42	$3.855\,025$	$4.600\,736$	$1.480\,743$	$10.080\,581$
			151	$1.868\,187$	$2.529\,758$	$0.764\,724$	$4.885\,158$
			359	$2.922\,446$	$3.709\,866$	$1.100\,429$	$7.641\,962$

Appendix

Table 10: Per-seed aggregate test metrics for PatchTST and TimeXer, grouped by asset, model, and timeframe. Timeframe labels are inferred from Tables 4 and 2 because the source CSV has no timeframe column.

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