Most-Recent Anchoring with Recurrent Ordering for Time Series Forecasting

Jung Min Choi; Ngoc Son Le; Ibram Abdelmalak; Vijaya Krishna Yalavarthi; Lars Schmidt-Thieme

cs.LGOct 2, 2026

Most-Recent Anchoring with Recurrent Ordering for Time Series Forecasting

Authors: Jung Min Choi, Ngoc Son Le, Ibram Abdelmalak, Vijaya Krishna Yalavarthi, Lars Schmidt-Thieme

Organizations: VWFS Data Analytics Research Center (VWFS-DARC), Hildesheim, Germany

Abstract

Long-term forecasting models commonly process all patches in a look-back window using the same fixed stack. Older contextual patches and recent evidence therefore receive the same computational depth. Yet the information closest to the forecast and the more distant context do not contribute equally. Uniform processing leaves this distinction unexpressed in the architecture. We propose MARO, a Most-Recent Anchoring with Recurrent Ordering model that processes the look-back window from the most recent patch to the oldest. The most recent patch serves as the anchor. It initializes the latent state and conditions each subsequent step, so older patches are folded into a representation that remains centered on recent evidence. A single shared module is reused at every step, so extending the scan further into the past introduces no additional parameters. Intermediate states retained during the scan allow the forecast head to weigh short and long portions of the history separately. This expresses recency through the order of recurrent refinement. Extensive experiments across multiple real-world time series datasets show that MARO achieves state-of-the-art performance on both long-term and short-term forecasting tasks.Ablation studies examine the contribution of the main architectural components.

Figures & tables

Panel of Figure 1 — Figure 1: Conventional patch mixers transform every patch at the same fixed depth in panel (a). MARO starts from the most recent patch and recurrently incorporates older patches in panel (b).

Panel of Figure 2 — Figure 2: Test MSE under old-to-recent and recent-to-old scanning with causal attention and RNN updates. Recent-to-old scanning gives lower MSE in all four comparisons.

Panel of Figure 3 — Figure 3: Overview of the MARO architecture.

Panel of Figure 4 — Figure 4: Recurrent processing from the most recent patch to the oldest. The anchor and future context condition every update. Selected intermediate states and the refined final state are fused into $\bar{z}$ .

	MARO (Ours)		SRSNet		TimeKAN		Amplifier		iTransformer		TimeMixer		PatchTST
Dataset	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETT (Avg)	0.329	0.372	0.335	0.375	0.340	0.380	0.346	0.383	0.351	0.384	0.346	0.383	0.343	0.381
Weather	0.223	0.261	0.225	0.265	0.226	0.269	0.223	0.263	0.230	0.269	0.225	0.262	0.223	0.262
Electricity	0.155	0.252	0.160	0.254	0.163	0.257	0.162	0.255	0.162	0.258	0.184	0.281	0.170	0.270
Traffic	0.372	0.265	0.391	0.270	0.419	0.285	0.412	0.290	0.397	0.280	0.409	0.278	0.396	0.275
Solar	0.186	0.245	0.183	0.238	0.198	0.263	0.202	0.281	0.201	0.260	0.203	0.260	0.200	0.284

Table 1: Long-term results averaged over

H\in\{96,192,336,720\}

, with the four ETT subsets merged into one group. Full per-dataset, per-horizon results and standard deviations are reported in Appendix C .

		MARO (Ours)		CycleNet/MLP		iTransformer		SCINet		PatchTST
Dataset	$H$	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
PEMS03	12	0.064	0.168	0.066	0.172	0.071	0.174	0.066	0.172	0.099	0.216
	24	0.083	0.190	0.089	0.201	0.093	0.201	0.085	0.198	0.142	0.259
	48	0.131	0.239	0.136	0.247	0.125	0.236	0.127	0.238	0.211	0.319
	96	0.188	0.298	0.182	0.282	0.164	0.275	0.178	0.287	0.269	0.370
PEMS04	12	0.075	0.179	0.078	0.186	0.078	0.183	0.073	0.177	0.105	0.224

Table 2: Full PEMS forecasting results. Baseline values are quoted from the published CycleNet comparison.

	ETTh1		ETTh2		Weather		Electricity
Variant	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Full MARO	0.396	0.423	0.316	0.373	0.223	0.261	0.153	0.252
w/o calendar	0.406	0.432	0.333	0.381	0.223	0.263	0.161	0.255
w/o channel mixing	0.408	0.433	0.371	0.408	0.224	0.261	0.157	0.256
w/o inter-patch mixer	0.422	0.440	0.332	0.380	0.228	0.266	0.157	0.255
w/o intra-patch mixer	0.407	0.431	0.337	0.384	0.228	0.266	0.168	0.263

Table 3: MARO component ablations averaged over

H\in\{96,192,336,720\}

. Values are truncated to three decimal places. The best value in each column is bold and the second best is underlined. The full model is a repeated-seed mean, each ablation one validation-selected seed.

Dataset	$H$	Recent-to-old (MARO)	Old-to-recent
ETTh1	96	0.3554	0.3816
	336	0.3959	0.3951
ETTm1	96	0.2842	0.3136
	336	0.3599	0.3846
Weather	96	0.1460	0.1558
	336	0.2442	0.2592

Table 4: Test MSE of the two complete traversal conventions on ETTh1, ETTm1, and Weather. Recent-to-old traversal anchors at the most recent patch and scans toward the oldest. Old-to-recent traversal anchors at the oldest patch and scans toward the most recent. Lower is better.

Panel of Figure 5 — Figure 5: Computational-efficiency comparison under the common protocol detailed in Appendix A.3 . Both axes use logarithmic scales. Points closer to the lower-left require fewer FLOPs and have lower inference latency. Bubble size encodes peak training memory, and color identifies the model.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Domain	$C$	$T$	Sampling	Split (train/val/test)
ETTh1 ( Zhou et al., 2021 )	Transformer load	7	17,420	1 hour	8,640 / 2,880 / 2,880
ETTh2 ( Zhou et al., 2021 )	Transformer load	7	17,420	1 hour	8,640 / 2,880 / 2,880
ETTm1 ( Zhou et al., 2021 )	Transformer load	7	69,680	15 min	34,560 / 11,520 / 11,520
ETTm2 ( Zhou et al., 2021 )	Transformer load	7	69,680	15 min	34,560 / 11,520 / 11,520
Weather ( Max Planck Institute for Biogeochemistry, 2024 )	Meteorology	21	52,696	10 min	36,887 / 5,270 / 10,539
Electricity ( Trindade, 2015 )	Power demand	321	26,304	1 hour	18,412 / 2,632 / 5,260

Appendix

Table 5: Benchmarks used in this work.

C

is the number of variables and

T

is the number of time steps. The final column gives the chronological train-validation-test split.

Dataset	Model	Params	FLOPs	FLOPs/ $C$	Epoch	Latency	Memory
		(M)	(G)	(G/ch.)	(s)	(ms/sample)	(MB)
ETTh1 ( $C=7$ , batch size 32)
	DLinear	0.10	0.001	0.0001	0.62	0.004	21
	TimeKAN	0.05	0.028	0.0040	7.54	0.338	423
	iTransformer	0.95	0.021	0.0030	1.64	0.024	47
	PatchTST	0.94	0.134	0.0191	1.91	0.052	162

Appendix

Table 6: Measured cost of MARO and four representative baselines under a common protocol with

L=512

and

H=96

on one RTX 4060 Laptop GPU. Params counts trainable parameters, FLOPs is the forward cost of one sample and FLOPs

/C

the same quantity per input channel, Epoch is the wall-clock time of the first training epoch, Latency is the evaluation-mode forward time per sample, and Memory is the peak allocation during training. ETTh1 uses batch size 32, Electricity uses batch size 4, and Weather uses batch size 16. Lower is better throughout.

Quantity	Symbol	Range or value
Learning rate	$\eta$	log-uniform, $[1\times 10^{-5},5\times 10^{-3}]$
Look-back length	$L$	$\{96,336,512\}$
Token width	$d$	$\{32,64,128,256,512\}$
Inter-patch hidden width	$d_{\mathrm{ff}}$	$\{64,128,256,512,1024\}$
Latent MLP layers	$L_{e}$	integer in $[1,4]$
Intra-patch MLP layers	$L_{d}$	integer in $[1,4]$

Appendix

Table 7: Unified Optuna search space for MARO.

Dataset	$H$	$L$	$P$	$S$	$d$	$d_{\mathrm{ff}}$	$L_{e}$	$L_{d}$	$R$	Dropout	$\eta$	$\lambda$	$B$
ETTh1	96	512	64	32	32	1024	1	1	1	0.014	$2.645\times 10^{-4}$	$1.0\times 10^{-5}$	256
ETTh1	192	512	64	32	32	1024	1	4	0	0.082	$3.677\times 10^{-4}$	0	256
ETTh1	336	512	144	108	64	64	1	1	2	0.129	$6.353\times 10^{-4}$	$1.0\times 10^{-7}$	256
ETTh1	720	336	112	84	128	128	1	1	1	0.267	$1.812\times 10^{-3}$	$1.0\times 10^{-3}$	256
ETTh2	96	512	32	16	32	512	4	1	3	0.320	$4.370\times 10^{-4}$	0	256
ETTh2	192	512	128	64	32	1024	1	1	3	0.166	$6.428\times 10^{-4}$	$1.0\times 10^{-6}$	256

Appendix

Table 8: Best MARO backbone and optimization configurations for the long-term benchmarks. Here

\lambda

denotes weight decay.

Dataset	$H$	$P$	$S$	$d$	$d_{\mathrm{ff}}$	$L_{e}$	$L_{d}$	$R$	Dropout	$\eta$	$\kappa$	$\kappa/(C\!-\!1)$	$d_{g}$	$\beta$	$g_{\mathrm{ch}}$ init	$g_{r}$ init	$B$
PEMS03	12	96	29	64	256	3	4	1	0.133	$2.523\times 10^{-3}$	320	0.896	64	2.00	$8.30\times 10^{-3}$	0.100	16
PEMS03	24	12	6	64	512	1	3	0	0.109	$4.786\times 10^{-3}$	320	0.896	4	0.00	$5.01\times 10^{-3}$	0.100	16
PEMS03	48	12	9	256	1024	1	3	0	0.109	$8.417\times 10^{-4}$	6	0.017	128	2.00	$3.02\times 10^{-3}$	0.200	16
PEMS03	96	32	10	128	1024	1	3	0	0.185	$2.426\times 10^{-3}$	100	0.280	64	2.00	$4.75\times 10^{-3}$	0.010	16
PEMS04	12	12	6	512	1024	1	2	1	0.197	$1.794\times 10^{-3}$	32	0.105	4	2.00	$1.91\times 10^{-2}$	0.200	16
PEMS04	24	48	36	128	1024	2	4	2	0.034	$2.284\times 10^{-3}$	100	0.327	64	1.00	$2.64\times 10^{-2}$	0.025	16

Appendix

Table 9: Best MARO configurations for the PEMS benchmarks.

Dataset	$H$	$\kappa$	$\kappa/(C\!-\!1)$	$d_{g}$	$\beta$	$g_{\mathrm{ch}}$ init	$g_{r}$ init
ETTh1	96	2	0.333	16	1.00	$8.93\times 10^{-4}$	0.200
ETTh1	192	6	1.000	8	0.00	$1.38\times 10^{-2}$	0.010
ETTh1	336	6	1.000	32	1.00	$4.72\times 10^{-2}$	0.100
ETTh1	720	2	0.333	16	1.00	$3.66\times 10^{-4}$	0.010
ETTh2	96	5	0.833	128	2.00	$3.99\times 10^{-3}$	0.050
ETTh2	192	5	0.833	4	0.50	$6.16\times 10^{-3}$	0.010

Appendix

Table 10: Best MARO channel-mixer and gate configurations for the long-term benchmarks.

		MARO (Ours)		SRSNet		TimeKAN		Amplifier
Dataset	Horizon	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.354 $\pm 0.0005$	0.390 $\pm 0.0004$	0.366	0.394	0.370	0.396	0.373	0.399
	192	0.391 $\pm 0.0008$	0.411 $\pm 0.0010$	0.400	0.415	0.403	0.417	0.414	0.420
	336	0.398 $\pm 0.0019$	0.429 $\pm 0.0027$	0.424	0.430	0.420	0.432	0.442	0.446
	720	0.440 $\pm 0.0030$	0.460 $\pm 0.0024$	0.426	0.455	0.442	0.465	0.455	0.467
Avg		0.396	0.423	0.404	0.423	0.408	0.427	0.421	0.433

Appendix

Table 11: Full long-term forecasting results. The remaining baselines are shown in Table 12 .

		MARO (Ours)		iTransformer		TimeMixer		PatchTST
Dataset	Horizon	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.354 $\pm 0.0005$	0.390 $\pm 0.0004$	0.386	0.405	0.372	0.401	0.377	0.397
	192	0.391 $\pm 0.0008$	0.411 $\pm 0.0010$	0.430	0.435	0.413	0.430	0.409	0.425
	336	0.398 $\pm 0.0019$	0.429 $\pm 0.0027$	0.450	0.452	0.438	0.450	0.431	0.444
	720	0.440 $\pm 0.0030$	0.460 $\pm 0.0024$	0.495	0.487	0.483	0.483	0.457	0.477
Avg		0.396	0.423	0.440	0.444	0.426	0.441	0.418	0.435

Appendix

Table 12: Full long-term forecasting results continued from Table 11 .

Cell	Learned	Random fixed	Correlation fixed
Electricity $H{=}96$	$.12724\pm.00025$	$.12679\pm.00005$	$\mathbf{.12579\pm.00073}$
Electricity $H{=}336$	$\mathbf{.16202\pm.00162}$	$.16514\pm.00285$	$.16738\pm.00266$
Solar $H{=}96$	$.16597\pm.00261$	$.16466\pm.00560$	$\mathbf{.16386\pm.00200}$
Solar $H{=}336$	$\mathbf{.18707\pm.00277}$	$.19922\pm.00190$	$.18878\pm.00098$
Traffic $H{=}96$	$.34486\pm.00584$	$\mathbf{.33564\pm.00056}$	$.33966\pm.00018$
Traffic $H{=}336$	$.38336\pm.00403$	$\mathbf{.38083\pm.00140}$	$.38601\pm.00030$

Appendix

Table 13: Channel-topology controls. Entries are test MSE over three seeds and bold marks the lowest mean in each row.

Cell	Frozen $\Delta$	LayerScale $\Delta$	Wide $\Delta$	Separate ctx. gate $\Delta$
ETTh1 $H{=}96$	$+.000010$	$-.000031$	$-.000002$	$+.000015$
ETTh1 $H{=}336$	$+.000009$	$+.000040$	$-.000015$	$+.000052$
ETTh2 $H{=}96$	$-.000388$	$+.000350$	$+.000494$	$+.000546$
ETTh2 $H{=}336$	$-.000015$	$+.000055$	$-.000011$	$-.000006$
Weather $H{=}96$	$+.000863$	$+.000936$	$+.001294$	$+.000671$
Weather $H{=}336$	$-.000307$	$-.000263$	$-.000241$	$-.000052$

Appendix

Table 14: Gate controls. Entries are three-seed mean MSE changes from the corresponding baseline and negative is better.

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Dual-Context Analog Retrieval for Time Series Forecasting

Jung Min Choi, Ngoc Son Le, Ibram Abdelmalak, Vijaya Krishna Yalavarthi+1

ISMLL, University of Hildesheim · VWFS Data Analytics Research Center (VWFS-DARC), Hildesheim, Germany

Long-Term Time Series Forecasting Time Series Forecasting Retrieval-Augmented Time Series Forecasting

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Most long-term time-series forecasting models map the look-back window directly to the full horizon in a single pass. While efficient, this design does not explicitly identify which historical states are most relevant to different future segments or exploit what followed those states. Analog forecasting addresses this by retrieving past states similar to the present and using their observed continuations, but single nearest matches can be unreliable and overlapping patches may produce redundant candidates. We propose DuoTS, a Dual-Context Time Series forecasting model that uses retrieved evidence without relying on it exclusively. DuoTS first produces a base forecast with a parallel patch encoder and linear prediction head, then progressively refines it one future patch at a time. Each refinement combines two views: a current context that attends to recent tokens and captures the latest dynamics, and a detail context that provides distinct retrieved analogs together with their subsequent trajectories. Patch-wise refinement allows the model to balance these views across the forecast horizon and associate each future segment with evidence appropriate to its temporal distance from the present. Experiments on multiple real-world datasets show that DuoTS achieves state-of-the-art performance, while ablations confirm the contribution of each context. The refinement mechanism is also model-agnostic, requiring only an encoded look-back window and the future-patch position, and can therefore be integrated into existing forecasting models.

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