Enhancing Multivariate Time Series Forecasting with Global Temporal Retrieval

• Global cycles can be harder to capture than local patterns because they unfold over long spans and may be obscured by non-stationarity, noise, missing data, or extreme values.Their predictive signal can exceed that of adjacent temporal patterns.Source: §1 · pp. 1–2
• Extending the look-back window risks overfitting to noise, increases computational and memory costs, and makes relevant long-term signals harder to distinguish from redundant data.Source: §1 · p. 2
• GTR retrieves cycle-aligned segments from an adaptive global embedding, combines them with local input through 2D convolution, and uses residual fusion without changing the host architecture.Source: §1 · pp. 2–3
• Across six benchmarks and short- and long-term settings, GTR improves diverse forecasting backbones and achieves overall state-of-the-art accuracy with minimal parameter and runtime overhead.Source: §1 · p. 3

Modeling Periodicity of Time Series

• Decomposition and FFT-based methods model periodic components, while CycleNet learns recurrent cycles, but these approaches can remain bounded by observed history or stationary-cycle assumptions.Source: §2 · p. 3

2D-Variations of Time Series Modeling

• 2D methods use CNNs, MLPs, or structured transformations to capture complex temporal features, yet they lack a consistent mechanism for aligning representations with global cycles.Source: §2 · p. 3

Retrieval-/Memory-Augmented Forecasting

• Retrieval-augmented forecasting fetches similar segments from history or external repositories, but depends on similarity-search quality and does not itself provide compact, time-aligned representations of very long cycles.Source: §2 · p. 3

3.1 PROBLEM STATEMENT AND OVERVIEW

• The method focuses on forecasting when the global cycle is much longer than the historical input, and processes an enhanced representation with a forecasting backbone.Source: §3.1 · p. 4

3.2 GLOBAL TEMPORAL RETRIEVER

• GTR learns a global temporal embedding for each variable, uses absolute cycle position to retrieve aligned references, and applies 2D convolution and residual fusion to combine global and local patterns.The embedding is a trainable parameter matrix initialized to zero; the convolution kernel uses the dominant high-frequency period length P.Source: §3.2 · pp. 4–5

3.3 BACKBONE AND PROJECTION STRUCTURE

• The forecasting backbone used in this work is a lightweight MLP that projects the GTR representation, applies two linear layers with GeLU and a residual connection, then maps features to the forecast horizon.Source: §3.3 · p. 5

3.4 METHOD DETAILS

• RevIN normalizes each input batch using instance-specific mean and variance and reverses that operation on outputs; GTR preserves input dimensionality for backbone integration.The stated total complexity is O(NT^2 + Nd^2 + NTd + NSd), linear in N and S.Source: §3.4 · pp. 5–6

4.1 EXPERIMENT SETUP

• The evaluation uses six datasets, MSE and MAE, a historical length of 96, and four prediction horizons per dataset group, comparing GTR with recent forecasting models.The PEMS horizons are 12, 24, 48, and 96; other datasets use 96, 192, 336, and 720.Source: §4.1 · p. 6

4.2.1 LONG-TERM FORECASTING

• Across 16 long-term tasks, GTR ranked top two in 10; on Solar-Energy it reduced MSE by 8.2% and MAE by 6.5% versus CycleNet.On traffic datasets, GTR had higher MSE than S-Mamba, SOFTS, and iTransformer.Source: Table 1 · p. 6, §4.2.1 · p. 6

4.2.2 SHORT-TERM FORECASTING

• Across 8 short-term tasks, GTR ranked top two in all; versus iTransformer it reduced MSE by 18.7% and MAE by 12.1% on average across datasets and horizons.Against S-Mamba, it achieved 15.7% MSE and 9.6% MAE reductions.Source: Table 2 · p. 7, §4.2.2 · p. 7

4.3 ABLATION STUDIES AND ANALYSIS

• GTR improved all evaluated models across datasets and prediction horizons, with especially pronounced traffic gains, including PEMS04 MSE reductions of 91.9% for DLinear and 56.2% for PatchTST.It also reduced MLP-backbone average MSE by 14.4% on Electricity, 55.1% on PEMS03, and 73.5% on PEMS04; integration during training was described as trivial.Source: Table 3 · p. 7, §4.3 · p. 7
• Across look-back lengths, GTR outperformed baselines, with the largest gains at the shortest windows; on Electricity and Solar-Energy, baseline errors rose exponentially as windows shrank while GTR degraded marginally.Forecast horizons were fixed at 336 for Electricity and Solar-Energy and 96 for PEMS03 and PEMS04.Source: §4.3 · pp. 7–8, Figure 3 · p. 8
• GTR uses 40.1K parameters and 4.50M MACs alone; GTR with an MLP uses 0.98M parameters and 306.91M MACs, 19.0% of iTransformer’s parameter count.The combined system takes 22.3 seconds per epoch, compared with 18.1 seconds for DLinear.Source: Table 4 · p. 8, §4.3 · p. 8
• Across four datasets, GTR-enhanced multivariate correlations aligned more closely with dataset-wide ground-truth correlations; the authors report improved robustness to non-stationary disturbances.Source: §4.3 · p. 8

Correlation Visualization

• Figure 4 compares pre- and post-GTR multivariate correlations with global correlation structures across four datasets.The visualization uses Pearson correlation coefficients and reports closer alignment after GTR.Source: Figure 4 · p. 9

Fixed Cycle-Length Assumption

• GTR assumes one fixed cycle length across the input and channels, which may be suboptimal for time-varying or heterogeneous periodicity.It may also underperform when a series has a single dominant periodicity.Source: §5 · p. 9

Challenges in Modeling Long-Range Cycles

• Learning yearly or multi-year cycles typically requires decades of continuous, high-quality data, which real-world settings rarely provide.For large P, convolution complexity is O(NTP), kernel parameters scale linearly with P, and memory overhead and overfitting risk increase.Source: §5 · p. 9

Scalability with Long Input Sequences

• GTR’s T × T linear projection has O(NT^2) complexity, making the module inefficient for long input sequences.The module is designed for short look-back windows.Source: §5 · p. 9

Future Work

• Future work is motivated in adaptive cycle modeling, handling cross-channel periodic heterogeneity, and efficiently learning extreme long-horizon periodicity.The limitations identify scenarios where GTR may not be the optimal solution.Source: §5 · p. 9

• Across six real-world datasets, GTR delivers state-of-the-art performance in both short-term and long-term forecasting scenarios.Source: §6 · p. 9
• GTR is a lightweight, plug-and-play module that lets forecasting models use temporal information from the entire cycle.Source: §6 · p. 9
• The work addresses the limitation that existing MTSF models’ historical context prevents effective capture of global periodic patterns.Source: §6 · p. 9

• The authors report no potential ethical risk because the work focuses only on time-series forecasting.Source: §7 · p. 10

8 REPRODUCIBILITY STATEMENT

• The model architecture is formalized with equations in the main text.Source: §8 · p. 10
• The Appendix contains implementation details, including dataset descriptions, metrics, model, and experiment configurations.Source: §8 · p. 10
• The code has been made public.Source: §8 · p. 10

A.1 DATASETS DETAILS

• The six dataset groups cover transformer, weather, electricity, traffic, solar-energy, and PEMS time series.The descriptions include sampling intervals and domains; PEMS data are aggregated at five-minute intervals, or 288 points per day.Source: §A.1 · p. 14

A.2 METRIC DETAILS / A.3 EXPERIMENT DETAILS

• Long-term forecasting is evaluated with MSE and MAE, while the experiments use a global cycle length L selected from domain knowledge or autocorrelation peaks.A significant autocorrelation peak at lag k supports choosing L=k; selected lengths are listed in Table 6.Source: §A.2 · p. 15, §A.3 · p. 15, Table 6 · p. 15

A.3 EXPERIMENT DETAILS

• The experimental protocol uses PyTorch on one NVIDIA RTX 3090 GPU, Adam, and baseline hyperparameters from the original publications.For the GTR ablation, the module was added to baselines configured for T=96 and trained end-to-end without further hyperparameter optimization.Source: §A.3 · p. 15

B MORE DETAILS OF GTR

• GTR indexes a learnable global-cycle embedding by absolute position, aligns it with the normalized input, then applies 2D convolution and residual fusion before the host forecaster.The host model receives the fused representation without architectural modification, and GTR and host parameters are jointly trained.Source: B MORE DETAILS OF GTR · p. 16

C.1 FULL FORECASTING RESULTS

• GTR achieves comprehensive state-of-the-art results across the full multivariate forecasting benchmarks with look-back length T=96.Table 7 reports results for all prediction horizons; the best and second-best results are marked.Source: §C.1 · p. 16, Table 7 · p. 17

C.2.1 IMPACT OF REVERSIBLE INSTANCE NORMALIZATION

• Across most datasets, removing RevIN worsens performance, with ETTh2 at horizon 720 increasing in MSE from 0.423 to 0.872.The authors retain RevIN as the default despite Electricity and Solar cases where removing it performs better, potentially because zero-value segments bias its mean estimates.Source: §C.2.1 · pp. 17–18, Table 8 · p. 18

C.2.2 ANALYSIS OF EXTRACTION VARIANTS

• The original 2D convolution achieves the best MSE in 19 of 40 cases and the best MAE in 18, with the most consistent overall performance among extraction variants.The comparison includes point-wise fusion, Inception, and 1D convolution alternatives.Source: §C.2.2 · pp. 18–19
• The authors attribute point-wise fusion's weaker performance to its lack of a temporal receptive field, and hypothesize that 2D convolution better aligns local and global rows than 1D convolution.They also suggest the Inception variant's added parameters may overfit shorter sequences, or that one suitably sized kernel captures the dominant periodicity.Source: §C.2.2 · pp. 18–19

C.2.3 CAPABILITY WITH INTER-CHANNEL MODELING

• GTR augmented with inter-channel modeling is presented as an adaptable option for traffic data, where strong inter-variable dependencies challenge its channel-independent design.The authors report that adding GTA lets GTR reach state-of-the-art performance on datasets where those relationships matter.Source: §C.2.3 · pp. 19–20
• The authors report that adding Global Token Aggregation substantially reduces MSE across Traffic prediction horizons by incorporating inter-variable context.GTA distills channel relationships into a global token and broadcasts it back to guide channel predictions; Table 9 presents the comparison.Source: §C.2.3 · pp. 19–20, Table 9 · p. 20

C.3 ERROR BAR ANALYSIS

• Across five random-seed runs, GTR's MSE and MAE standard deviations are mostly below 0.001 across datasets and forecasting horizons.Figure 5 fixes look-back length and forecasting horizon at 96; Table 10 reports full results.Source: §C.3 · p. 20, Figure 5 · p. 20, Table 10 · p. 21

C.4 FULL RESULTS WITH LONGER LOOK-BACK WINDOW

• GTR achieves the best MSE in 19 of 32 metrics at T=336 and 15 of 32 at T=720 against baselines using longer look-back windows.The reported examples are a 13.2% MSE reduction over CycleNet on Solar-Energy at T=336 and a 6.7% MSE improvement over RAFT on Weather at T=720.Source: §C.4 · pp. 21–22, Table 11 · p. 22

C.5 COMPARISON WITH TIMESTAMP-BASED APPROACHES

• At prediction horizon T=720 on Electricity, GLAFF's iTransformer MSE is 0.5529, compared with 0.2178 for GTR.The comparison evaluates both modules with DLinear and iTransformer on Electricity and Weather; the authors report GTR is more robust in long-term forecasting.Source: §C.5 · pp. 22–23, Table 12 · p. 23
• GTR adds approximately 0.3 MB of memory on DLinear, compared with approximately 4.8 MB for the timestamp-based approach.The authors characterize GTR's memory overhead relative to the backbone as negligible.Source: §C.5 · p. 23

C.6 VISUALIZATION RESULTS

• Across PEMS visualizations, GTR is reported to fit future traffic variations more precisely than evaluated models and to reduce its MLP backbone's oversmoothing.The authors also report accurate trend forecasts in examples with little or no pronounced periodicity in the input.Source: §C.6 · p. 23, Figure 6 · p. 24, Figure 7 · p. 24

D.1 PROBLEM SETUP AND ASSUMPTIONS

• The theoretical setup models observed segments as periodic patterns plus Gaussian observation error and global embeddings as those patterns plus independent Gaussian embedding error.The stated observation and embedding error terms are mutually independent.Source: §D.1 · p. 26

D.2 GTR AS A BAYESIAN ESTIMATOR

• In the stated Bayesian framing, inference combines observed segments and global embeddings through a linear combination treated as a posterior-mean estimator.The passage identifies the observations as likelihood information and the embeddings as prior information.Source: §D.2 · p. 26

D.3 THEORETICAL RESULT

• GTR is reported to systematically reduce correlation-estimation error between variables by fusing global information sources.The theoretical analysis compares correlations before and after GTR processing and presents Figure 4 as empirical illustration of reduced error.Source: §D.3 · pp. 26, 28

E EXTENDED RELATED WORK

• The authors identify a gap in existing plug-and-play methods: they lack a dedicated mechanism for retrieving global periodic patterns when the look-back window is shorter than the cycle.They present GTR as a solution that retrieves and uses global temporal patterns beyond the host model's immediate receptive field.Source: E EXTENDED RELATED WORK · p. 29