Improving Time Series Forecasting via Instance-aware Post-hoc Revision
Authors: Zhiding Liu
Mingyue Cheng
GuanHao Zhao
Jiqian Yang
Qi Liu
Enhong Chen
Venue: NeurIPS 2025 poster ()
Keywords: Time Series Forecasting
Post-Processing
Primary area: applications

Abstract: Time series forecasting plays a pivotal role in various real-world applications and has attracted significant attention in recent decades. While recent methods have achieved remarkable accuracy by incorporating advanced inductive biases and training strategies, we observe that instance-level variations remain a significant challenge. These variations—stemming from distribution shifts, missing data, and long-tail patterns—often lead to suboptimal forecasts for specific instances, even when overall performance appears strong. To address this issue, we propose a model-agnostic framework, PIR, designed to enhance forecasting performance through Post-forecasting Identification and Revision. Specifically, PIR first identifies biased forecast instances by estimating their predictive accuracy. Based on this, the framework revises the forecasts using contextual information, including covariates and historical time series, from both local and global perspectives in a post-processing fashion. Extensive experiments on real-world datasets with mainstream forecasting models demonstrate that PIR effectively mitigates instance-level errors and significantly improves forecasting reliability.

Improving Time Series Forecasting via Instance-aware Post-hoc Revision
Zhiding Liu', Mingyue Cheng', Guanhao Zhao', Jiqian Yang', Qi Liu', Enhong Chen
'Staee Key Laboratory of Cognitive Intelligence, University Science and Technology of China (zhiding ghzhao0223, yangiq) www.mmmmauuutee..eeeaaaaaaaa ustc. edu. cn (mycheng, qiliuql, (heneh)Gustee edu. cn
Abstract
Time series forecasting plays a vital role in various real-world applications and has attracted significant attention in recent decades. While recent methods have achieved remarkable accuracy by incorporating advanced inductive biases and training strategies, we observe that instance-level variations remain significant challenge. These variationss-ttemminng from distribution shifts, missing data, and long-tail patterns-oftet lead to suboptimal forecasts for specific instances, even when overall performance appears strong. To address this issue, we propose a model-agnostic framework, PIR, designed to enhance forecasting performance through Post-forecasting Identification and Revision. Specifically, PIR first iden- tifies biased forecasting instances by estimating their accuracy. Based this, the framework revises the forecasts using contextual information, including co- variates and historical time series, from both local and global perspectives in post-processing fashion. Extensive experiments on real-world datasets with main- stream forecasting models demonstrate that PIR effectively mitigates instance-level errors and significantly improves forecasting reliability. Our code is available
Introduction
Time series forecasting is fundamental task in time series analysis, attracting considerable attention Various applications have been facilitated by the advancement of forecasting, including traffic planning
in recent years 40 49
[7]. stock market prediction [23]. healthcare analytics [19) and weather
forecasting 3 59 Recent years have witnessed significant efforts dedicated to this area, with deep learningbbased approaches achieving remarkable success due to their powerful ability to capture both
temporal [62] 63 and cross-channel dependencies [60] 30). Furthermore, advanced inductive biases and training strategies have been introduced to address the non-stationary nature of time series data 20 33
and to construct foundation models for time series forecasting 9 32 52).
Despite their satisfactory performance in overall evaluations, we emphasize that existing forecasting approaches often overlook inherent instance-level variations, which can arise from the long-tail distribution of numerical patterns in time series data and ultimately lead to forecasting failures in specific cases. Specifically, time series typically represent the numerical reflections of complex and dynamic real-world systems and are therefore prone to noise, sensor failures, and other anomalies during data collection. These issues can result in potential distribution shifts [26), missing values [2]. or unforeseen anomalies 4 Therefore, while most instances exhibit similar numerical patterns, a subset may present rare behaviors, and mainstream forecasting methods often struggle to effectively model these exceptional instances, leading to inaccurate even unreliable forecasting outcomes.
Enhong Chen is the corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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1.4-
1.0
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(a) Per-instance MSE Curve
(b) MSE Distribution
Figure 1: Per-instance MSE evaluation of PatchTST on the ETTh1 dataset and its corresponding error distribution. The error varies among instances and exhibits a long-tail distribution due the instance-level variations.
To better illustrate this phenomenon, we present the per-instance Mean Squared Error (MSE) eval- uation curve of PatchTST (37 on the ETThl dataset [62]. along with the corresponding error distribution visualized through both a histogram and kernel density estimate in Figure | in the figure, while the MSE remains consistently low for the majority of instances, there exist specific cases where PStchTST yields unsatisfactory forecasting results, as indicated by multiple spikes in the error curve. Moreover, the distribution clearly exhibits long-tail pattern, reinforcing our motivation and underscoring the challenges posed by the instance-level variations.
As shown
To this end, we propose the PIR framework, designed to enhance forecasting results via Post- forecasting Identification and Revision, addressing the challenge from novel post- post-procsssing perspective. The framework comprises two key components. The first is the failure identification mechanism, which identifies the potential biased forecasting instances where the model's predictions less reliable, through estimating the forecasting performance second a post-revision module, which refines the forecasts by leveraging contextual information from both local and global perspectives. For the local revision, inspired by exogenous variable modeling approaches [38 [50). we utilize immediate forecasts of covariates along with available exogenous information such as timestamps (45) and textual descriptions 277 side information implicitly mitigate the impact of instance-level variations within a local window. This approach is grounded in the assumption that dependencies between covariates like lead-lag effects can provide valuable insights into future trends [61]. and exogenous information can serve as additional prior conditions guiding the revision. For the global revision, the framework addresses rare or atypical numerical patterns by explicitly retrieving similar instances from the global historical data (28). This retrieval-basee based strategy enables the model better capture long-tail patterns that may be overlooked by conventional forecasting models. Finally, PIR integrates the original forecasts with its revision outputs a weighted sum, making it model aggnosic and broadly compatible with existing forecasting architectures. The primary contributions of our work are summarized as follows:
per-instance level. The
We are the first to highlight the existence of instance-level variations that can lead to forecasting failures certain cases, evident by the unsatisfactory performance of existing forecasting methods at the per-instance level.
We introduce PIR, a model-agnostic framework designed to address this challenge. The framework estimates the forecasting performance to identify the potential failures and utilizes contextual information to revise them from both local and global perspectives.
We conduct extensive experiments on well-established real-world datasets, covering both long-term and short-term forecasting settings with mainstream models. The results demon- strate that the PIR framework consistently enhances forecasting accuracy, leading to more reliable and robust performance.

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2 Related Work
2.1 Time Series Forecasting
Time series forecasting has been central area of research for several decades. One of the earliest landmark contributions was the development of statistical methods, which are celebrated for their solid theoretical foundation and systematic approach to model design. Representative works in this domain include ARIMA and Holt- Winters [5] 181, which have laid the groundwork for more advanced methodologies. More recently, with the advancement of deep learning, numerous neural forecasting models have been proposed, achieving superior performance. Recurrent Neural Networks (RNNs) are among the first deep learning architectures applied forecasting [51 41), followed by variety of other structures, such as convolution-base models 21 35 7 attention-based networks
22 24 [3] and MI.P-based architectures [39 [5 23]. These models have demonstrated remarkable
capabilities in capturing both temporal and cross-channel dependencies within time series data, leading to substantial improvements in forecasting accuracy.
Beyond advancements in model architecture, a range specialized techniques rooted time series analysis has also emerged. These include methods for time series decomposition [54] [56] frequency
modeling [55]. and approaches for non-stationary forecasting (20) [3), which address the unique challenges presented by time series data. Besides, self-supervised pretraining has gained significant attention as a powerful approach, with various training strategies being explored [53] 6. 58 In
addition, recent efforts aim construct foundational time series models capable of learning universal representations and being applied to diverse downstream tasks 34
9 32 52 Moreover, some
pioneer works explore forecasting enhanced with the reasoning ability of LLMs 46 36).
2.2 Context Modeling in Time Series Forecasting
In addition to forecasting based solely on multivariate time series data, several pioneering studies have explored the incorporation of contextual information to enhance forecasting performance [. On one hand, some advancements focus integrating exogenous information within a local window during the forecasting process. For instance, TFT [24) and TiDE [8] leverage dense encoders to process timestamp information, which is subsequently used to condition future forecastings. Similarly, NBEATSx 38 and TimeXer (50) improves the forecasting accuracy of target variables by explicitly modeling the influence of exogenous variables. On the other hand, some studies investigate the potential of retrieving relevant time series from the global historical context. RATD (28) utilizes the
retrieved series references to guide the denoising process of diffusion-basse forecasters, and RATSF 48 introduces the retrieval augmented cross-attentinn architecture for explicitly modeling similar historical data. More recently, RAFT [14) achieves satisfactory performance through forecasting enhanced with multi-period retrieval.
Different from existing methods, our proposed PIR framework tackles a novel research challenge: mitigating the impact of instance-level variations that can lead to forecasting failures in certain cases. The framework begins by identifying the potential failure instances through estimating their accuracy, and then revises the forecasts by leveraging available contextual information from both local and global perspectives in a post-processing manner. As result, PIR functions as model- model-agnostic plugin, allowing it to be seamlessly integrated into arbitrary forecasting models for enhanced performance.
3 Methodology
In this section, we will delve into the specifics of the proposed PIR framework, which is illustrated in Figure We begin with the problem definition, followed by a comprehensive description of the framework's s key components.
3.1 Problem Definition
We first consider the general multivariate time series forecasting task. Given a set of input series X JMM the objective is to learn mapping function Y fo( that accurately forecasts the future values Y M where x; Ig Nx represents the i-th input time series and
3

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Global Revising
Histonccl
Selevent Time
Fulereiia
Seriin
Simiartty Metric
Top K Similarities
Input Series Mx
Uncernans Estinater
Projection
Projection
Indicators e goxo
Results
y E R Ri
LuNE SPY
Emngenou
Variables
Loyder
Intormediate F 2
Local Revising
Figure 2: Overview of the proposed PIR framework. The framework first identifies the potential forecasting failure cases through estimating the performance the intermediate results generated by backbone models Global Revising components, which utilize contextual information, including available exogenous variables within the local window and global historical time series, to revise the forecasting results for enhanced performance.
per-instance level. Besides, the framework incorporates Local Revising and
U: E TR Nout represents the corresponding target series, Here, N denotes the number of channels and M is the number of instances, while Lin and Lout denote the lengths of the input and target series, respectively. For simplicity and brevity, we will omit the indices for the time series instances in the following sections.
Moreover, the PIR framework focuses novel problem to revise the forecasting results for better performance. Specifically, given the intermediate results arbitrary forecasting models, the objective is learn the revising function Y = fX, Y, C)) that corrects the potential forecasting failures. Here, C represents the available contextual information, such as exogenous variables, that aid in the revision process for more accurate and reliable forecasts.
3.2 Failure Identification
The goal of the PIR framework is to post-process forecasting results by identifying and revising potential forecasting failures caused by instance-level variations. Thus, the identification process becomes primary target and challenge. Conceptually, it forms an Uncertainty Estimation task based on the immediate forecasting results. Though various efforts have been devoted in this area, it has not been deeply explored for properly estimating the uncertainty of point-wise forecasting results mainly due to two reasons. Firstly, given the regression nature of the forecasting task, most existing approaches generate predictions directly from the hidden states. As a result, token-level distributions before generation are not available, and common uncertainty evaluation methods based on probabilities are not directly applicable [1]. Secondly, the forecasting failures arise from both data uncertainty (e.g., missing values) and model uncertainty (c.g., underfitting on long-tail patterns) 12
while most existing uncertainty quantification methods primarily focus on the latter one.
Although have identified several potential reasons that may lead to prediction failure, there are many other potential and interrelated factors, and there is lack of ground truth and metrics to identify and disentangle the specific reasons for each forecasting failure instance. Therefore, we not explicitly locate these failure patterns. Instead, we innovatively quantify uncertainty using forecasting error and adopt a data-driven approach as practical solution for estimating the uncertainty of given input-forecast pair (x, 7). which is more flexible and potentially accommodate a broader

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range of failure modes. Specifically, following common practice in modeling complex dynamics [0 we employ a two-layer fully connected neural network with non-linear activation functions (.) to estimate the forecasting uncertainty. Additionally, we introduce auxiliary constraint to support the abovementioned procedure. Since explicit uncertainty is not directly available for the forecasting results, we treat the forecasting error as feasible guiding signal. The intuition behind this is that higher uncertainty will likely result in greater forecasting error. Therefore, the estimated uncertainty is further constrained to predict the MSE of the forecasting results:
6 = Sue (2r, U, E),
N
Lu N 16 18 1-
Here 5 is the estimated uncertainty, and ||-1/1 represents the Mean Absolute Error (MAE) loss function, which ensures that the estimated uncertainty aligns with the actual forecasting error. To provide additional contextual information, we introduce the channel embedding matrix E = (e) C2 ..... CN) RNxd, which encodes the channel identity information. This matrix enables the model to better capture variations across different channels and provides crucial context for more accurate uncertainty estimation. Through this approach, the framework can generate uncertainty estimates specific to each model and input instance, thereby satisfying both types of uncertainty. Moreover, it forms a coupled framework, enabling efficient end-to-end optimization jointly with the forecasting task, and offers degree of interpretability by using the forecasting error as a measurement for uncertainty.
3.3 Local Revising
After identifying the potential forecasting failures with high uncertainty, the PIR framework revises these results from both local and global perspectives. For the local revision component, the core idea is to leverage the contextual information within local horizon window, which includes the intermediate forecastings of covariates and available exogenous variables, to enhance forecasting accuracy. The intuition behind this approach is straightforward. Firstly, the dependencies including lead-lag effects are widely present in the time series data, where the forecasting results of covariates can provide valuable insights into future trends 61.. Besides, the exogenous variables, such as the time-related information and environmental factors known advance can serve as a prior condition mitigating the impact of sudden distribution shifts caused by natural rhythms like holiday Conceptually, this approach particularly beneficial for models that prioritize robustness over capacity by adopting channel-independen strateg [33
24
45
effects
15 +
In practice, we project the intermediate forecasting results into hidden states on per-variate basis [30]. along with the available exogenous variable information, which are concatenated for further correlation extraction. Let hew. hezo be the representation of covariates and exogenous variables respectively, and e refer to the available exogenous variable information corresponding to the instance, the projection process formulated as:
Ho = [heos hezo],
hoo Co CoVaiiatEEmb(())
hazo = ExoVariateEmb(().
Here Co Co)aratteEmb()) a trainable linear projector, and Exo VariateEmb()) implemented flexibly based on the characteristic of which can be a linear projector for numerical features language models for textual descriptions (27). Through this approach, local context from multiple sources and domains can be seamlessly embedded in the framework to guide the revising process.
The hidden states are then passed through a traditional Transformer [44] with a linear prediction head to generate the revised results Ptocal. By leveraging the attention mechanism, the local revision component explicitly captures the correlations between covariates and exogenous variables, thereby ensuring that the contextual information within the local window is fully utilized to correct forecasting failures and enhance prediction accuracy.
3.4 Global Revising
In addition, the PIR framework incorporates a global revision component that leverages global historical information to further refine forecasting results. As illustrated in Figure instance-level
5

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variances can lead to a long-tail distribution in performance, primarily because traditional models struggle to capture rare numerical patterns. To address this challenge, we introduce straightforward yer effective retrieval module that explicitly retrieves relevant historical time series exhibiting similar numerical characteristics. These retrieved series serve as reference signals during the revision process, enabling the model to better handle atypical patterns that are typically underrepresented in training.
Specifically,, we first construct the retrieval database using only the training input-target time series pairs (Xtrain, Ytrain), as we treat historical information as the global context. This design not only prevents data leakage but also facilitates the extension of the database to incorporate multi-source datasets, since it depends solely on raw time series data. Based on the retrieval database, the top-K most relevant time series are selected for a given imput series x by computing the similarity between x and each candidate in the database, as formalized below:
Index, w =Top Sim Ene(z), Enc(X)),
Yrc- = (Vtrain,/VVe E Index).
Here, Enc(-) is an encoding function that processes the time series, which is instantiated as an instance normalization operation [20] in practice for its simplicity and effectiveness of mitigating the impact of non-stationarity that could lead to unstable similarity estimation. Moreover, powerful pre- trained forecasting models [9] 32 52 can be optionally utilized for better representation projection. Additionally, w represents the top- K similarity scores estimated by the similarity operator Sim(., +), which is instantiated using cosine similarity due to its computational efficiency.
Once the relevant time series are retrieved, they serve as references for revising the forecasting results. Instead of modifying the architecture of the backbone forecasting models to incorporate these references, we adopt a practical assumption: similar instances tend to exhibit similar future trends. Therefore, the retrieved references themselves can serve as effective estimations for the target series. This design ensures that the framework remains entirely independent of the backbone models, making it applicable to any forecasting model. In practice, the similarity scores are treated as importance indicators, and the global revised results Yglobal are generated through weighted sum operation, formulated as follows:
p Softmax(w).
Vglobal WeightedSuum(p. Yre),
where the Softmax(-) function ensures that Σ P: = 1, assigning higher weights to retrieved instances that are more similar to the input series.
3.5 Optimization Target
By combining the components described above, the PIR framework produces the final forecasting results through fost-forecasting identification and revision using a residual approach [16]
Upred īj + Offoccat + Byglobol,
o (Linear(0)),
(5)
3 (MTP((6 w)).
Here, a and / are learned weights corresponding to the local and global revision components, respectively, and o(-) denotes the Sigmoid activation function. A linear transformation is employed to estimate a, with its weight and bias initialized to vectors of ones and zeros. This design ensures ensuring a positive correlation that higher uncertainty estimates lead to larger values of o, thus placing greater emphasis on the local revision. In contrast, , is generated through a multi-layer perceptron (MLP), which takes both the estimated uncertainty and the retrieval similarities as input. This allows the model to dynamically adjust the influence of the global revision based on the confidence of the prediction and the relevance of the retrieved historical series. The overall optimization objective is to minimize the MSE between the revised forecasts and the ground truth, formulated as:
Cpr
1
Σ
I|ypeed v112.
(6)
Finally, let À denote the weight hyperparameters for the auxiliary constraint defined in Section 3.2 the overall optimization objective for the PIR framework is then formulated as multitask learning problem:
C Cpr + XLue

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4 Experiments
In this section, we conduct extensive experiments on widely used benchmark datasets, comparing our proposed PIR framework with mainstream forecasting approaches under both long-term and short-term forecasting settings, to demonstrate its effectiveness.
Table I: Forecasting performance under long-term and short-term settings. The results are averaged from all the target series lengths, and the full results are provided in the Appendix. The bold values indicate better performance.
Methods
PatchTST
PIR
[mp.(%)
SparseTFF
+ PIR
Imp.(%)
iTrans.
PIR
Imp.(*)
TimeMixer
PIR
Imp.(%)
MSE
0.466
0.437
6.22
0.444
0.433
2.48
0.451
0.432
4.21
0.445
0.429
3.60
ETThl
MAE
0.452
0.439
2,88
0.431
0.429
0.46
0.445
0.437
1.80
0.436
0.431
1.15
MSE
0.384
0.375
2.34
0.384
0.373
2,86
0,383
0.377
1.57
0.380
0.378
0.53
ETTh2
MAE
0.405
0.400
1.23
0.403
0.398
1.24
0.406
0.403
0.74
0.405
0.403
0.49
MSE
0.397
0.383
3.53
0.416
0.378
9.13
0.407
0.383
5.90
0.381
0.377
1.05
ETTml
MAE
0.408
0.397
2.70
0.407
0.390
4.18
0.412
0.397
3.64
0.396
0.393
0.76
MSE
0.281
0.283
-0.71
0.287
0.281
2.09
0.291
0.288
1.03
0.276
0.274
0.72
ETTm2
MAR
0.329
0.330
-0.30
0.329
0.328
0.30
0.334
0.334
0.00
0.322
0.323
-0.31
MSE
0.215
0.200
6.98
0.224
0.196
12.50
0.179
0.175
2.23
0.185
0.181
2.16
Electricity
MAR
0.303
0.279
7.92
0.297
0.275
7.41
0.269
0.265
1.49
0.275
0.270
1.82
MSE
0.269
0.244
9.29
0.385
0.275
28.57
0.236
0.231
2.12
0.231
0.223
3,46
Solar
MAR
0.307
0.287
0.370
0.296
20.00
0.263
0.260
1.14
0.270
0.267
MSE
0.259
0.254
1.93
0.276
0.261
5.43
0.260
0.255
1.92
0.245
0.244
0.41
Weather
MAR
0.281
0.277
1.42
0.294
0.282
4.08
0.280
0,277
1.07
0.274
0.274
0.00
MSE
0.482
0.459
4.77
0.637
0.477
25.12
0.425
0.420
1.18
0.519
0.492
5.20
Traffic
MAR
0,308
0.299
2.92
0.379
0.314
17.15
0.283
0,280
1.06
0.307
0.291
5.21
MSE
0.158
0.120
24.05
0.351
0.154
56.13
0.115
0.107
6.96
0.089
0.089
0.00
PEMS03
MAE
0,265
0.231
12.83
0.400
0.261
34.75
0.225
0.216
4.00
0.200
0.200
0.00
MSE
0.206
0.140
32.04
0.370
0.171
53.78
0.108
0.097
10.19
0.083
0.081
2.41
PEMS04
MAE
0.305
0.251
17.70
0.419
0.278
33.65
0.220
0.206
6.36
0.191
0.190
0.52
MSE
0.165
0.115
30.30
0.352
0.149
57.67
0.095
0.089
6.32
0.087
0.083
4.60
PEMS07
MAE
0,268
0.223
16.79
0.404
0.249
38.37
0.198
0.189
4.55
0.191
0.187
2.09
MSE
0,186
0.147
20.97
0.362
0.180
50.28
0.147
0.135
8.16
0.130
0.128
1.54
PEMS08
MAB
0,284
0.251
11.62
0.413
0,279
32.45
0.245
0.237
3.27
0.238
0.232
2.52
4.1 Experimental Setup
Datasets. For the long-term forecasting task, conduct experiments widely recognized bench- mark dataset that includes eight real-world datasets spanning diverse domains [54] 21]. Additionally,
we incorporate the PEMS dataset, which contains four subsets, for the short-term forecasting task 29). The exogenous information used in these datasets are the available timestamps. We also conduct experiments on datasets with additional textual descriptions in the Appendix. Following standard experimental protocols, we split each dataset into training, validation, and testing sets in chronological order. The split ratios set to 6:2:2 for the ETT dataset and 7:1:2 for the other datasets. Detailed information about the datasets is available in the Appendix.
Backbone Models. PIR is model-agnostic plugin that can be seamlessly integrated with any time series forecasting model. To demonstrate the effectiveness of the framework, we select four mainstream forecasting models based on diverse architectures, encompassing both channel- channel-dependent and channel-indeependent assumptions, as backbones. These models are evaluated under both long- term and short-term forecasting settings: PatchTST (37), Sparse TSF [25) I'Transfrmmer [30] and TimeMixer [7).. We implement these models following their official code.
Experiments Details. We employ the ADAM optimizer as the default optimization algorithm across all experiments and evaluate performance using two metrics: mean squared error (MSE) and mean absolute error (MAE). For the PIR framework, the retrieval number K is tuned from the set (10, 20, 50). and the weight hyperparameter À is fixed at All experiments are conducted on a single NVIDIA RTX 4090 GPU.
7

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GroundFiuth Estimation Errer
GroundTruch Estimation Error
1.0
0.250
0.225
0.200
0.175
0.4
will
0.125
0.2
0.100
200
400
600
800
1000
200
400
600
800
1000
(a) Solar
(b) Traffic
Figure 3: Comparison of the groundtruth forecasting error and the estimation of PIR on Solar and Traffic dataset. The backbone Sparse and the target length is 336.
4.2
Main Results
we set the input series length 7.n. = 96 across all datasets. For a unified comparison, the target series length Lout is set to {12, 24, 36, 48} for the PEMS dataset and {96, 192, 336, 720} for the remaining datasets. The forecasting results for both long-term and short-term settings, along with the corresponding relative performance improvements, are summarized in Table
Following the standard evaluation protocol 62 56
As shown in the table, the proposed PIR framework consistently improves the performance of state- of-the-art forecasting models across most scenarios in both long-teng term and short-term forecasting settings. This improvement primarily due to PIR's capability to identify potential forecasting failures and effectively leverage contextual information for revision. Specifically, across all 48 experimental settings, PIR achieves an average MSE reduction of 8.99 for PatchTST. Similar trends are observed for other backbone models, with reductions of 25.87% % for Sparse 3.47 % for iTransformer, and 2.34% for TimeMixer. These results underscore the generalizability of the PIR framework, demonstrating its seamless integration with diverse forecasting models, regardless of their architecture or inductive biases, to deliver enhanced predictive performance.
Additionally, we observe that the relative performance improvements for channel-dependent ap- proaches are smaller compared to those for channel-indeper inneeedddnd models. This likely because channel-dependent methods already incorporate covariate information, resulting in stronger baseline performance and leaving less room for improvement. Nevertheless, by leveraging the forecasted covariates, future exogenous variables, and historical time series contextual information, the PIR framework still manages to enhance the performance of these models. Notably, although the local revision component of PIR shares a structural resemblance with iTransformer, it continues to yield substantial relative improvements. These findings further support our hypothesis that instance-level variations contribute to forecasting failures in specific cases. Moreover, the comparison also high- lights the importance of post-forecet forecatnng failure identification and revision in generating more reliable and robust forecasting results.
4.3 Qualitative Analysis
To better illustrate how the PIR framework works to help enhance the forecasting performance, provide a qualitative analysis of the identification and revision process in this section.
We begin by evaluating the reliability of the failure identification component through a comparison backbone models and PIR's 's estimated error, as defined
between the actual forecasting error in Equation [I] Specifically, we visualize both metrics over a segment of the test set from the Solar and Traffic datasets, using SparseTSFF as the backbone model, in Figure The results demonstrate that the PIR framework accurately estimates the forecasting error of the backbone's 's intermediate predictions.

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(b) SparseT5F
(c) (c)TTrasfommr
(dI TimeMixer
Figure 4: Illustration of the per-instance MSE distribution differences for four mainstream forecasting approaches, both with and without the enhancement of PIR. The MSE values corresponding to the peak density are also highlighted. The comparisons are performed on the ETThl and PEMS07 datasets, with the target length set to 96 and 48.
Notably, the estimated and actual error curves exhibit consistent patterns in terms of peaks and troughs, which validates PIR's capability to assess the quality of individual forecasting results. This strong alignment underscores the effectiveness of PIR's 's uncertainty estimation mechanism and its ability to reliably identify potential forecasting failures, laying solid foundation for the subsequent revision stage.
For the revision component, although the quantitative results reported in Table [ demonstrate its effectiveness in improving overall forecasting performance, we further investigate how the PIR framework mitigates the effects of instance-level variance. Specifically, we evaluate the per-instance MSE of the baseline backbone models on the ETTh1 and PEMS07 datasets. As illustrated in Figure 4 we compare the MSE distribution with and without PIR enhancement, measured using kernel density estimation, and highlight the MSE corresponding to the peak density for each case. The figure reveals that models enhanced by PIR yield more reliable forecasting results, their error distributions exhibit higher density at lower MSE values. Additionally, the MSE corresponding to the peak density is significantly reduced. Additionally, PIR framework also effectively addresses forecasting failures, substantially reducing errors for instances poorly modeled by the backbone models. This improvement is particularly evident the PEMS07 dataset, where the tail of the error distribution curve shifts significantly toward smaller MSE values. For example, the maximum prediction error of Sparse on ETTh] decreases from 2.85 0.81 when enhanced with PIR.
In summary, the qualitative analysis strongly aligns with our expectations. The PIR framework can effectively identify forecasting failures and enhance overall performance by revising the intermediate results in a model-agnostic manner.
4.4 Complexity Analysis
In this section, we analyze the computational overhead of the proposed PIR framework from both theoretical and empirical perspectives. Theoretically, the series-wise cosine similarity function used in the retrieval stage has a time complexity of O(N M(NMLan) where N denotes the number of channels, M is the total number of historical series per channel, and Lin represents the input sequence length. The subsequent local revision process involves channel attention operations, resulting in a complexity of O(N2). To further evaluate the practical efficiency of PIR, we report the average inference time on both small-scale dataset (ETTh1) and large-scale dataset (Traffic). We compare two retrieval strategies: brute-force cosine similarity and approximate retrieval using Locality-Sensitie Hashing (LSH). The results are summarized in Table 2

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Table 2: Inference time comparison under different settings.
ETThI(LSH) (CTs)
Traffic(Cos)
Traffic(LSH)
(ackone(s)
0.164
0.164
0,424
0.424
Aretrieval(s)
0.024
0.415
0.079
87.957
Arevision(s) 0.096
0.096
0.275
0.275
MSE Improvement
0.014
0.009
0.025
0.025
The results indicate that the retrieval stage introduces negligible additional latency on both datasets, thanks to the GPU-parallelizable nature of cosine similarity. For even larger datasets, the total computational cost can be further reduced by applying sampling strategies (e.g., stride sampling) or dimensionality reduction techniques to limit the search space. In contrast, the L.SH-based retrieval implemented with the f faiss library yields significantly higher inference time without performance gains, indicating that brute-force cosine similarity is both more efficient and effective in our current implementation.
5
Conclusion
In this paper, we first investigated the challenge of instance-level variance in time series forecasting, which often results in unreliable predictions for certain cases. To address this, we proposed the PIR framework, a model-agnostic solution that enhances the accuracy through post-forecasting identification and revision of potentially biased predictions. The framework identifies the forecasting failures by estimating their еrror on per-instance basis, and leverages contextual information to revise forecasts from both local and global perspectives. Extensive experiments across various benchmarks and forecasting models demonstrated that PIR consistently improves performance, highlighting its effectiveness and versatility as plug-in component for a wide range forecasting architectures. wish our work could raise new research directions for the forecasting task.
6 Acknowledgement
This work was supported by the National Natural Science Foundation of China (No. U23A20319, No. 62502486). We furthermore thanked the anonymous reviewers for their constructive comments.
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A Dataset Descriptions
In this paper, we leverage a diverse of forecasting datasets covering various domains evaluate the effectiveness of the proposed PIR framework under both long-term and short-term forecasting settings. We also include datasets with additional textual information [27 validate the framework's generalizability. The brief descriptions and characteristics are presented as follows:
The dataset records temperature and load metrics from electricity transformers, tracked between July 2016 and July 2018. It is subdivided into four mini-datasets, with data sampled either hourly or every 15 minutes.
E
Electricity The dataset captures the hourly electricity consumption kWh of 321 clients, monitored from July 2016 to July 2019.
S The dataset records the solar power production in the year of 2006, which is sampled every 10 minutes from 137 PV plants in Alabama State.
Weather The dataset records the 21 weather indicators, including air temperature and humidity every 10 minutes from the Weather Station of the Max Planck Biogeochemistry Institute in 2020.
Traffid The dataset provides the hourly traffic volume data describing the road occupancy rates of San Francisco freeways, recorded by 862 sensors.
P The dataset is a series of traffic flow dataset with four subsets, including PEMS03, PEMS04, PEMS07, and PEMS08. The traffic information is recorded at a rate of every minutes by multiple sensors.
Energy and Health These two datasets are subsets Time-MMD (2 multimodal time series dataset that ensures fine-grained alignment between textual and numerical modalities. The datasets are collected weekly, spanning from 1996 and 1997 up to May 2024, respectively.
Table 3: The overview of each dataset used in the experiments.
Dataset
Variables
Frequency
Length
Scope
ETTh &ETTh2
Hour
17420
Energy
7
15 Minutes
69680
Energy
Electricity
321
Hour
26304
Energy
Solar
137
10 Minutes
52560
Nature
Weather
21
10 Minutes
52696
Nature
Traffic
862
Hour
17544
Transportation
PEMS03
358
Minutes
26208
Transportation
PEMS04
307
5 Minutes
16992
Transportation
PEMS07
883
Minutes
28224
Transportation
PEMS08
170
5 Minutes
17856
Transportation
Energy
1 Week
1479
Energy
Health
11
1 Week
1389
Health
B Full Experimental Results
In this section, we present the complete long-term and short-term forecasting results in Table 4 These results demonstrate that the proposed PIR framework functions as a model-agnostic plugin,
hhtt://wwww.nrllgoowgggge hhtp://pemss.oo..c.gom
21

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Table 4: Full experimental results of long- and short-term forecasting. The target length Lout is chosen as (12,24.36,48) ) for the PEMS dataset and (96, 19,3332,33))) for the others. The bold values indicate better performance.
Methods Metric
PatchTST
PIR
SparseTSF
PIR
iTransformer
PIR
TimeMixer
+ PIR
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.410
0.416
0.375
0.400
0.399
0,401
0.375
0.392
0.385
0.403
0.376
0.402
0.384
0.399
0.370
0.397
192
0.458
0.443
0.422
0.427
0.438
0,423
0.420
0.416
0.440
0.434
0.424
0.429
0.432
0.425
0.422
0.421
336
0,498
0.464
0.467
0,451
0.478
0,443
0,465
0.440
0,486
0.457
0.465
0,450
0.486
0,449
0,460
0,442
720
0.498
0.486
0.484
0.477
0.461
0.457
0.473
0.466
0.494
0.485
0.461
0.466
0.476
0.470
0.464
0.462
96
0.299
0.347
0.291
0.340
0.304
0.347
0.289
0.338
0.302
0.350
0.298
0.346
0.295
0.343
0.291
0.343
E7Th2
192
0,384
0.398
0.371
0.391
0.386
0,396
0,373
0.392
0.382
0.399
0.374
0.396
0,378
0.398
0.367
0.395
336
0.424
0.432
0.418
0,429
0.424
0.429
0.418
0.426
0.423
0.433
0.415
0.429
0.421
0.436
0.422
0.431
720
0..427
0.444
0.421
0.441
0.421
0.438
0.412
0.435
0.424
0.443
0.420
0.440
0.:427
0.441
0,430
0,444
0,336
0.375
0.317
0.354
0.357
0.375
0.350
0,342
0.377
0.315
0.356
0.316
0.355
0.309
0.351
ETTm2 E1Tml
192
0.376
0.394
0.365
0,383
0.394
0,392
0,355
0.374
0,381
0.395
0.358
0,380
0.364
0,383
0.359
0.381
336
0.409
0.416
0.394
0.404
0.426
0.414
0.389
0.396
0.420
0.420
0.395
0.406
0.389
0.403
0.387
0.402
720
0.465
0.445
0.457
0.445
0.486
0.447
0.457
0.438
0.486
0.456
0.465
0.447
0.455
0.441
0.451
0.440
96
0.177
0.263
0.175
0.259
0.185
0,267
0.174
0.258
0.184
0.267
0.179
0.263
0.175
0.257
0.170
0.254
192
0.242
0.305
0.241
0.306
0.248
0,306
0.239
0.301
0.254
0.313
0.246
0.307
0.239
0.299
0.239
0.300
336
0.304
0.345
0.304
0.347
0.308
0.343
0,304
0.345
0,312
0,350
0.311
0,351
0.298
0.339
0.296
0.340
720
0.401
0.401
0,410
0.401
0,4008
0.398
0,408
0.407
0.412
0.440
0.417
0.415
0.393
0.394
0.389
0.397
Blectricity
96
0.193
0.284
0.180
0.253
0.210
0,280
0.174
0.250
0.148
0.240
0.145
0.237
0.156
0.248
0.151
0.244
192
0.198
0.289
0.184
0.262
0.206
0.281
0.180
0.259
0.163
0,254
0.161
0.251
0.170
0.261
0.165
0.258
336
0.214
0.304
0.198
0.278
0.219
0.195
0.276
0.177
0.270
0.175
0.268
0.187
0.277
0.186
0.275
720
0,255
0.336
0.239
0.322
0.260
0,329
0.233
0.314
0,227
0.311
0.219
0.303
0.227
0,312
0.221
0.307
96
0.233
0.287
0.210
0.263
0.336
0.351
0.231
0,270
0,205
0.238
0.196
0.235
0.198
0.261
0.195
0.248
Solar
192
0.266
0.307
0.241
0.286
0.376
0.371
0.272
0.292
0,237
0.262
0.235
0.257
0.241
0.274
0.238
0.275
336
0.291
0.317
0.261
0,297
0.415
0,384
0.330
0.313
0,251
0.275
0,248
0.275
0.253
0,274
0.235
0.273
720
0.286
0.316
0.263
0,300
0.413
0,374
0.297
0.310
0,250
0.276
0.246
0.274
0.231
0.271
0.225
0.271
96
0.119
0.220
0.168
0.208
0.201
0.240
0.175
0.218
0,174
0.214
0.170
0.211
0.163
0,210
0.161
0.208
Weather
192
0.225
0.259
0.216
0.253
0.242
0,273
0.220
0.256
0,222
0.255
0.217
0.252
0.208
0.252
0.206
0.250
336
0,279
0.298
0.276
0,297
0,294
0,308
0,284
0.302
0,281
0.299
0.277
0,298
0,266
0.291
0.263
0.291
720
0.354
0.347
0.355
0.350
0.366
0,355
0.364
0.353
0,361
0.352
0,356
0.350
0.341
0.343
0.344
0.347
96
0,459
0.298
0,428
0.288
0.664
0.395
0,454
0.306
0,393
0,268
0.390
0,266
0.489
0,296
0.453
0.275
PEMSI4 PEMS03 Traffic
192
0.468
0.301
0.450
0.294
0.611
0,366
0.456
0.302
0.415
0.277
0.415
0.278
0.495
0.299
0.473
0.285
336
0.483
0.307
0.466
0.299
0.619
0.367
0.480
0,313
0.429
0.284
0.426
0.283
0.533
0,311
0.503
0.294
720
0.518
0.326
0.493
0.315
0.655
0.387
0.516
0.333
0,461
0,301
0.447
0.299
0.557
0,322
0.539
0.309
0.085
0.196
0.074
0.183
0.145
0,258
0.081
0.191
0.069
0.174
0.067
0.172
0.063
0.168
0.064
0.170
24
0,135
0.249
0.105
0.217
0.267
0,352
0,126
0.238
0,098
0.209
0.092
0,202
0
0.195
0.084
0.196
36
0.180
0.287
0.134
0.246
0,416
0,449
0.178
0,285
0.130
0.243
0.119
0.231
0.099
0.213
0.099
0.212
0.231
0.326
0.165
0.276
0.574
0.541
0.229
0.328
0.164
0.275
0.149
0.260
0.110
0.224
0.110
0.223
12
0,106
0.218
0.089
0.198
0.158
0,274
0.096
0.207
0,081
0.189
0.077
0,182
0.070
0.174
0.069
0.173
24
0.170
0.279
0.122
0.235
0.286
0.374
0.143
0,256
0.099
0.211
0.090
0.199
0.079
0.186
0.078
0.185
0.239
0.337
0.156
0.268
0.436
0,468
0.194
0.301
0.119
0.233
0.105
0.216
0.086
0.195
0.085
0.193
0.310 48
0.386
0.191
0.301
0.601
0.561
0.250
0.347
0.134
0.248
0.116
0.227
0.097
0,210
0.094
0.207
PEMS07
12
0.080
0.190
0.070
0.175
0.131
0,248
0.075
0.180
0,066
0.160
0.065
0.161
0.059
0.157
0.057
0.155
24
0.134
0.246
0.101
0.210
0,262
0.354
0.120
0.228
0.088
0.191
0.083
0.183
0.077
0.181
0.076
0.179
0.193
0.295
0.130
0.240
0.423
0.459
0.167
0.272
0.105
0.211
0.097
0.199
0.095
0.201
0.094
0.200
0.253 48
0.339
0.157
0.266
0.593
0,556
0,233
0.314
0,121
0.228
0.110
0,213
0.115
0.224
0.106
0.214
PEMSO8
12 0.097
0.208
0.088
0.194
0.150
0,266
0.094
0.201
0.081
0.185
0.079
0.184
0.079
0.184
0.078
0.182
0.153
0.259
0.126
0.233
0.274
0.365
0.148
0.254
0.123
0,227
0.115
0.221
0.113
0.224
0.111
0.218
0.217
0.313
0.168
0.272
0.425
0.462
0.205
0.305
0.167
0.264
0.153
0.256
0.142
0.250
0.141
0.246
48
0.278
0.356
0.207
0.304
0.598
0,559
0.272
0.357
0.217
0.305
0.194
0.288
0.184
0.292
0.180
0.283
consistently improving the forecasting performance of various backbone models across diverse datasets and settings.
C Generalizability Investigation
In this section, we conduct comparative experiments on the Energy and Health datasets, which include additional aligned textual descriptions as exogenous information. These experiments aim to assess the generalizability of the proposed PIR framework in handling more complex contextual information. The results, presented in [ show that PIR consistently improves performance in most cases, thereby validating its effectiveness in multimodal forecasting scenarios.
22

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Table 5: Comparison experiments on the Energy and Health datasets. The input series length Lin set to 24, and the target length Lout is chosen as (12.24.36,48). The bold values indicate better
performance.
Methods Metric
PachTTT MSE
PIR
SparseTSF MSE
PIR
iransformer
+ PIR
TimeMixer MSE
PIR
MAB
MSB
MAE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MAE
MSE
MAE
0.194
0.255
0.255
0.122
0.245
0.242
Energy
24
0.299
0.418
0.248
0.364
0.252
0.375
0.241
0.362
0.242
0.365
0.232
0.355
0.226
0.348
0.222
0.346
0,382
0.327
0.309
0.314
0.463 48
0.527
0.425
0.49%
0.418
0.493
0.416
0.493
0.420
0.493
0.406
0.485
0.408
0.487
0.393
0.477
12.493
1.960
9
1.612
11.333
1,802
10.315
1.641
8.523
1.469
8.258
1.461
8.947
1.493
8.642
1.489
Health
24
1.5.552
2.204
13.486
1.924
14.115
2.077
13.837
1.975
12.159
1.801
11.698
1.748
12,010
1.789
11.790
1.765
36
13.804
2.130
12.032
1.893
12.856
2.052
12.876
1.969
11,662
1.854
11.093
1.793
11.385
1.801
11.029
1.792
2.001
1.781
10.328
1.784
D Ablation Study
In this section, we investigate the impact of the auxiliary constraint and structural designs on the overall performance of the PIR framework through ablation studies. The backbone models selected for this analysis are PatchTST and iTransformer, representing the channel-independen and channel- dependent categories, respectively.
PatchTSST
-Transformer
0.370
0.360
0.350
0.340
0.330
0.380
0.378
0.376
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
2
(a) MSE
(b) fue
Figure 5: MSE and the uncertainty estimation eтror, Lue, of PIR-enhanced PatchTST and iTrans- former on the ETTml dataset with different As.
Table 6: MAE comparison between different variants of the PIR framework. The Bold values indicate the best performance.
Backbone
PatchTST
iTrrasffrmmer
Variants
w/o PIR
w/o Local
w/o Global
w/
w/o Local
w/o Global
PIR
PEMS03 Electricity
96
0.284
0.257
0.270
0.253
0.240
0.238
0.241
0.237
192
0.289
0.266
0.277
0.262
0.254
0.253
0.256
0.251
336
0.304
0.282
0.292
0.278
0.270
0.268
0.272
0.268
720
0.336
0.326
0.325
0,322
0.311
0,305
0.304
0,303
12
0.196
0.201
0.192
0.183
0.174
0.175
0.174
0.172
0.249
0.243
0.228
0.217
0.209
0.204
0.207
0.202
36
0.287
0,281
0,262
0.246
0.243
0.234
0,239
0,231
48
0.326
0.314
0.298
0.276
0.275
0.262
0.272
0.260
To evaluate the impact of the auxiliary constraint, we compare forecasting performance across various values of the weight hyperparameter X, ranging from 0) to 1. Additionally, we report the corresponding uncertainty estimation error Lues as defined Equation] T in Figure The results
suggest that the auxiliary constraint enables the PIR framework to more accurately estimate the
23

---

uncertainty of intermediate forecasts by predicting their associated errors, thereby facilitating the revision weight learning, leading to better accuracy. Furthermore, the R-squared scores between MSE and Luee are 0.9067 and 0.7500 when PatchTST and I'Transfommer are used as the backbone models, respectively. These high correlations strongly support the feasibility of our approach, validating the use of forecasting error proxy for uncertainty in time series forecasting tasks.
On the other hand, we present the MAE comparison between different variants of the PIR framework on the Electricity and PEMS03 datasets in Table O providing an intuitive understanding of how the local and global revision components contribute to the performance. It can be inferred from the results that both components contribute to better performance compared to the baseline model under most cases, and the combination of them consistently leads the best accuracy, validating our proposal that utilizing contextual information to revise forecasting results from both local and global perspectives can well alleviate the impact of the instance-level variance.
To further examine where the performance gains of the PIR framework originate, we conduct an ablation study comparing PIR with two variants: (I) deepened iTransformer, which increases model depth to match the additional layers introduced by PIR's local revision component, and (2) PIR trained from scratch, which removes the requirement of pretrained forecasting backbone. The results on the Electricity and Weather datasets are presented in Table The results show that PIR consistently outperforms both variants. Benefiting from both global and local revision components, PIR effectively utilizes retrieved similar historical series as well as valuable contextual insights from covariates and exogenous variables. This allows PIR outperform simply enlarging model capacity, Furthermore, training PIR from scratch leads to degraded performance, possibly because the randomly initialized backhone produces unstable forecasts in early training stages, which negatively affects the optimization of the failure identification module and weakens its ability to estimate forecasting error.
Table 7: Investigation into the sources of performance improvement. The Bold values indicate the best performance.
Variants Metric
iTransformer MSE
w/ PIR
w/ Deepen
w/ PIR scratch
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.148
0.240
0.145
0.237
0.147
0.239
0.164
0.256
192
0.163
0.254
0.161
0.251
0.163
0.255
0.178
0.270
Electricity
336
0.177
0.270
0.175
0.268
0.177
0.271
0.196
0.284
720
0.227
0.311
0.219
0.303
0.217
0.304
0.256
0.334
96
0.174
0.214
0.170
0.211
0.177
0.218
0.217
0.249
192
0.222
0.255
0.217
0.252
0.224
0.257
0.252
0.270
Weather
336
0.281
0.299
0.277
0.298
0.279
0.296
0.300
0.315
720
0.361
0.352
0.356
0.350
0.358
0.350
0.393
0.371
E Forecasting showcases
In this section, we provide intuitive forecasting showcases to illustrate the impact of the revision process on forecasting performance, and the effect of global revision in cases with and without similar historical instances.
In Figure [. we examine the impact of the revision process on forecasting results using PStchTST as the backbone model across three datasets of varying scales. For the local revision component, struggles to capture scale changes using only cross-channel dependencies and exogenous information on the ETThl dataset, but successfully corrects trend deviations to better align with the ground truth on the Solar dataset. Meanwhile, the global revision component improves future scale predictions by retrieving similar historical series on the ETThl dataset but has minimal impact on the Solar dataset. Furthermore, both local and global revisions contribute to improved forecasting accuracy on the PEMS04 dataset, with their combination (i.e., the PIR framework) achieving superior performance. These findings indicate that local and global revisions each have their strengths and limitations, underscoring the importance of constructing a unified framework that effectively integrates both approaches.
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180
150
30c
380
159
150
209
Gruudiiz
2.-
1.
Solar
-044
-1.0
2.0
2.3
160
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PEMSI4
M wor M 2 20h
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-c.
-00
(a) Vd Local Revision
(b) w/ Global Revision
(c) W/ PIR
Figure 6: Illustration of forecasting showcases of different variants of PIR using PatchTST as the backbone model.
29 mm
Virhh Map
1.-
Avg. Amilaartty099955
(b) Avg. similariy=00.814
(c) Avg. similanttyy....o =0.384
-0606
=0.522
#0.446
PEMS10
In
6.-
3.3
Avg. similarity=0.996
(b) Avg. similantyy=0662
(c) Avg. similarty=00.229
=0.661
=0.553
=0.3449
Figure 7: Illustration of forecasting showcases on various forecasting instances with and without similar historical time series.
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Additionally, we evaluate the performance of global revision with and without similar historical instances. In Figure / we present the retrieval results Vyllobals as defined in Equation of our paper) as the forecasting outputs, along with the corresponding average top-k similarities and Tearned weight B. The results indicate that retrieval similarities vary significantly across instances. For instances with highly similar historical series, the retrieval process effectively captures future evolutions, whereas for those without close historical analogs, the retrieval results only approximate future trends and may even be inaccurate. This observation aligns with our expectations, the retrieval mechanism is designed to leverage similar past series as references for forecasting. Furthermore, the PIR framework adaptively assigns higher weights to instances with stronger retrieval similarities, dynamically adjusting the influence retrieval results on the final forecast.
Limitations
Though PIR demonstrates promising performance on benchmark datasets, there still several limitations within this framework. Firstly, the instance-level variances exist in both input series and target series, while the framework currently addresses only the former challenge. Identifying and addressing instance-level variances in the target series caused by data quality issues such as noise, outliers, and missing dota-holds significant potential for improving both the training and evaluation processes. Furthermore, relatively simple network architectures are utilized in the failure identification and local revision components. Exploring ways to integrate advanced inductive biases into these components to enhance their performance remains an important direction for future research.
26


Reviews:
[{"review_id": "HK1yCVeLJR", "reviewer": "Reviewer_X6vo", "summary": "This paper proposes a model-agnostic framework named PIR, which aims to enhance time series forecasting performance through post-forecasting failure identification and revision. PIR identifies biased forecasting instances by estimating their accuracy and revises the forecasts using contextual information, including covariates and historical time series, from both local and global perspectives. Extensive experiments on real-world datasets demonstrate that PIR effectively mitigates instance-level errors and significantly improves forecasting reliability.", "questions": "Seen in the weaknesses.", "limitations": "Seen in the weaknesses.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "strong\n(1) The PIR framework approaches the problem from a novel post processing perspective, focusing on identifying and revising forecasting failures, offering a unique solution in the field of time series forecasting. As a model agnostic plugin, PIR can be seamlessly integrated into any forecasting model, showcasing broad applicability and enhancing its versatility across different architectures.\n(2) Experimental results on multiple real world datasets and mainstream forecasting models indicate that PIR can significantly reduce forecasting errors, thereby improving the accuracy and reliability of predictions. In addition, this work provides the first in depth analysis of the performance of existing forecasting methods at the instance level, revealing the impact of instance level variations on forecasting failures and offering new insights for future research. And by estimating forecasting errors to quantify uncertainty and aligning it with actual prediction errors, PIR accurately identifies potential forecasting failure cases.\n\nweak:\n(1) Uses a 2-layer MLP but no exploration of advanced architectures (e.g., Transformers).\n(2) Brute-force similarity search and no approximate methods (e.g., LSH) for large-scale data.\n(3) α/β derived via Sigmoid without theoretical guarantees and fixed λ=1 may be suboptimal (Fig. 5).\n(4) Fixed input length (L_in=96) and untested on very long sequences (e.g., L_in>720). Also there is no variance across runs (e.g., random seeds).\n(5) No theoretical time complexity analysis (e.g., local revision’s Transformer cost, O(N) retrieval comparisons). The experiments mention \"single GPU\" but omit overhead comparison (e.g., retrieval latency, memory usage vs. base models).", "was_revised": true, "final_justification": "The answers have solved my concern", "rebuttal": "Thank you for your acknowledgement and valuable feedbacks on our work, we would like to address your concerns as follows.\n\n- [W1&W4] Thank you for raising these points. We would like to clarify a few aspects first. In our submitted manuscript, we followed common practice by employing a simple two-layer MLP to model complex dynamics for forecasting failure identification. The input length $L_{in}$ was set to 96 primarily to align with the experimental settings of prior works. Additionally, our main experiments were conducted over three runs, and we report only the average performance. This is due to the stability of recent forecasting models, where the variance across runs is typically negligible.\n\n  We also appreciate your suggestion to explore the generalizability of PIR under different uncertainty estimators and input settings. Below, we provide additional MSE results using PatchTST as the backbone on the ETTh1 dataset:\n\n  | ETTh1/MSE | $L_{in}$=96 |                   |                | $L_{in}$=720 |                   |                |\n  | --------- | ----------- | ----------------- | -------------- | ------------ | ----------------- | -------------- |\n  |           | PatchTST    | +Linear Estimator | +TRM Estimator | PatchTST     | +Linear Estimator | +TRM Estimator |\n  | 96        | 0.410       | 0.375             | 0.374          | 0.384        | 0.378             | 0.380          |\n  | 192       | 0.458       | 0.422             | 0.425          | 0.428        | 0.419             | 0.416          |\n  | 336       | 0.498       | 0.467             | 0.468          | 0.457        | 0.443             | 0.449          |\n  | 720       | 0.498       | 0.484             | 0.490          | 0.505        | 0.493             | 0.512          |\n\n  - First, increasing the look-back window generally improves the baseline model’s accuracy. When enhanced by our PIR framework, performance is further improved, demonstrating its generalizability across different input lengths.\n  - Second, we replaced the default linear estimator with a one-layer transformer block (with roughly tuned hyperparameters) for forecasting failure identification. The results show comparable performance across most settings. However, possibly due to overfitting induced by the transformer's increased capacity, it sometimes underperforms the simpler linear estimator. Specifically, for the case where $L_{in}=96$ and $L_{out}=720$, the estimation error $L_{ue}$ (defined in Eq.1 of our paper) on the test set is 0.1752 for the linear estimator, compared to 0.1770 for the transformer. The results demonstrate that the simple MLP layers can well handle the task of forecasting error estimation, validating the feasibility of our current implementation. \n\n- [W2&W5] We appreciate your suggestions of comparing with approximate methods for retrieving and including theoretical time complexity analysis for our framework.  Theoretically, the series-wise cosine similarity function used in the retrieval process has a complexity of $O(NML_{in})$, where $M$ is the total number of historical series for one channel and $N$ is the number of channels. Meanwhile, the local revision process has a complexity of $O(N^2)$ due to the channel-wise attention mechanism.\n  We further include inference time evaluations on both small-scale (ETTh1) and large-scale (Traffic) datasets using brute-force cosine similarity and LSH:\n\n  |                   | ETTh1(Cosine) | ETTh1(LSH) | Traffic(Cosine) | Traffic(LSH) |\n  | ----------------- | ------------- | ---------- | --------------- | ------------ |\n  | Backbone          | 0.164         | 0.164      | 0.424           | 0.424        |\n  | $\\Delta$retrieval | 0.024         | 0.415      | 0.079           | 87.957       |\n  | $\\Delta$revision  | 0.096         | 0.096      | 0.275           | 0.275        |\n  | $\\Delta$MSE       | -0.014        | -0.009     | -0.025          | -0.025       |\n\n  - Thanks to the GPU-parallelizable nature of cosine similarity, the retrieval process incurs negligible additional inference time on both datasets. Moreover, as analyzed before, for even larger datasets, we can introduce sampling strategies (such as stride) and embedding methods to reduce the total number of historical series and dimensionality to further limite the search space, therefore to reduce the time and memory overhead.\n  - Besides, we also implement the LSH method for similarity computing. Note that the current implementation stores $N$ databases and conduct similarity search using CPUs, therefore it requires much more additional time to retrieval time series data. Moreover, the results show that using the approximate method may only achieve just comparable performance with the cosine similarity, further demonstrating the feasibility of our current implementation.\n\n- [W3] \n\n  - As discussed in our response to [W1 & W4], the linear estimator effectively captures the immediate forecasting error $\\delta$, and the $\\alpha, \\beta$ derived via simple linear layers with sigmoid function ensures a strong correlation between these parameters. This enables effective guidance for the subsequent revision step. To be specific, the weights of $\\alpha$'s projectin learned on the ETTh1 dataset of 4 target lengths are [0.9579, 0.9620, 0.9699, 0.9776] respectively, ensuring a positive correlation between $\\alpha$ and $\\delta$. Besides, since the global revision process should take both the uncertainty and retreived similarity into account, we introduce a MLP layer to model the relationship. The case study in Fig7 illustrates that the PIR framework tends to allocate higher $\\beta$ for higher averaged similarities, which makes sense. Consequently, our approach effectively utilizes $\\delta$ as a guiding signal for the latter revision process.\n  - We agree that using a fixed $\\lambda=1$ may not be optimal. We plan to investigate adaptive strategies for determining $\\lambda$ in future work.\n\nWe hope our responses adequately address your concerns, and we sincerely appreciate the opportunity to clarify and improve our work. We will include the suggested experiments, discussions and in-depth cases in our revised paper."}, {"review_id": "JgxANlx7mR", "reviewer": "Reviewer_PruS", "summary": "The paper proposes a model-agnostic and extensible framework for improving time series forecasting. It identifies prediction failure cases through uncertainty estimation and addresses them from both local and global perspectives. Experimental results demonstrate the framework's effectiveness.", "questions": "- What is the specific retrieval process during model training? Does\nthe model start with a complete training set as the retrieval database, or does it use a slow-start mechanism to gradually accumulate data? Is the training process sequential or random? How do these differences affect the final results?\n- The framework shows significant performance variations across different models and datasets. Why are there differences between datasets and models? Does the model architecture (e.g., transformer- based or linear-based) have an impact?\n- Referring to the strengths and weaknesses section, could you provide more thorough analysis on the failure identification part? For example, more comprehensive theoretical support, how the lag effect of covariates works and to what extent it can identify different failure types, and case examples with more detailed analysis? Please note that since I consider this part critical to the paper, this response is crucial to me.", "limitations": "yes.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "strengths:\n- Easy to extend to existed methods.\n- The experimental results show effectiveness.\nWeaknesses:\n-  Limited improvement on strong baselines like timemixer\n- Lack of some training and experimental details and related analysis,\n   e.g., retrieval process (see questions for details)\n- Lack of theoretical or case analysis: Given the forecasting scenario,\nthe key to whether the entire framework works lies in whether prediction failure cases can be accurately identified in advance. Meanwhile, the revision stage methods are existing approaches in this field [1], so I pay more attention to the failure identification methods and related analysis. Unfortunately, the authors also use a simple method (mlp) here with insufficient theoretical analysis or case studies. Specifically, the paper classifies prediction failure causes but lacks detailed analysis of each category; the key factor proposed for uncertainty estimation is the lag of covariates, but this part also lacks in-depth discussion; finally, the paper only uses sample pairs and covariates to predict uncertainty, but its sufficiency remains questionable. For example, in distribution shift scenarios caused by weekdays and holidays, historical sequences alone may not be sufficient to identify prediction failures. Would incorporating timestamp changes or other external information as inputs for uncertainty prediction be more reasonable?\n[1] RATSF: Empowering Customer Service Volume Management through Retrieval-Augmented Time-Series Forecasting", "was_revised": true, "final_justification": "According to the authors’ rebuttal and additional experiments, I increase my score. Thanks for the additional explanation.", "rebuttal": "Thank you for your acknowledgement and valuable feedbacks on our work, we would like to address your concerns as follows.\n\n- [Q1&W2] To fully utilize the available time series data for better capturing the underlying data patterns, we use the entire training set as the retrieval database for training with a random process(termed as offline training). To avoid data leakage, we mask any portion of the historical data that overlaps with the query. Here we also investigate the impact of only retrieving on the previous time series data for a given query(termed as online training) as follows, and the results show that the online training strategy achieves comparable performance with the offline one:\n\n  |        |      | PatchTST |       | +PIR(offline) |       | +PIR(online) |       |\n  | ------ | ---- | -------- | ----- | ------------- | ----- | ------------ | ----- |\n  |        |      | MSE      | MAE   | MSE           | MAE   | MSE          | MAE   |\n  | ETTh2  | 96   | 0.299    | 0.347 | 0.291         | 0.340 | 0.292        | 0.343 |\n  |        | 192  | 0.384    | 0.398 | 0.371         | 0.391 | 0.371        | 0.394 |\n  |        | 336  | 0.424    | 0.432 | 0.418         | 0.429 | 0.420        | 0.431 |\n  |        | 720  | 0.427    | 0.444 | 0.421         | 0.441 | 0.425        | 0.443 |\n  | PEMS03 | 12   | 0.085    | 0.196 | 0.074         | 0.183 | 0.075        | 0.181 |\n  |        | 24   | 0.135    | 0.249 | 0.105         | 0.217 | 0.103        | 0.216 |\n  |        | 36   | 0.180    | 0.287 | 0.134         | 0.246 | 0.135        | 0.246 |\n  |        | 48   | 0.231    | 0.326 | 0.165         | 0.276 | 0.166        | 0.276 |\n\n- [Q2&W1] \n\n  - The backbone architecture indeed plays a significant role in forecasting accuracy, with simpler models (e.g., linear-based) generally underperforming more advanced ones. As a plug-in method, the strength of our PIR framework lies in its ability to improve forecasting accuracy across a variety of backbones while also mitigating performance variance caused by architectural differences. This explains why our method yields substantial improvements on certain models, while the gains on others are relatively modest. \n  - As for the performance differences across datasets, we attribute this to inherent characteristics of each dataset. While PIR addresses instance-level variations often overlooked by prior methods, it cannot fully account for uncertainties stemming from dataset construction—such as imputation or smoothing— which may cap the achievable performance. These data-specific factors may introduce an upper bound on the achievable accuracy, which may in turn limit the performance improvement attainable by our method.\n\n- [Q3&W3]\n\n  - Thank you for pointing out the related work. We will include a detailed discussion of the RATSF method in the revised paper. While both RATSF and our PIR framework leverage retrieval-based designs to enhance forecasting, the key difference lies in our design goals: PIR is a model-agnostic, post-processing framework that revises initial forecasting results from any backbone. To achieve this, we introduce both global and local revision components—via weighted aggregation of retrieved series and cross-channel attention over covariates and exogenous variables—making PIR fundamentally different from RATSF.\n  - We agree with your insight that the failure identification component is critical in our work. Although we have identified several potential reasons that may lead to prediction failure, there are many other potential and interrelated factors, and there is a lack of ground truth and metrics to identify and disentangle the specific reasons for each forecasting failure instance. **Therefore, we do not aim to explicitly locate these patterns to identify forecasting failures**. Instead, we define failure instances as those with high forecasting errors, which are then prioritized for revision. This approach is more flexible and can potentially accommodate a broader range of failure modes. Besides, we appreciate your suggestion to incorporate external information into the failure identification module. However, such information is often only relevant for a limited subset of failure cases, and incorporating them may introduce noise. Therefore, our current design relies solely on the original time series, immediate forecasts, and channel indicators to maintain robustness. We plan to explore more sophisticated strategies in future work.\n  - To further validate the effectiveness and rationality of our proposal of using MLP for failure identification, we present the comparison experiment of transformer-based uncertainty estimator as follows. The results demonstrate that the simple MLP layers can well handle the task of forecasting error estimation. Moreover, the estimation error $L_{ue}$, defined in Eq1 in our paper, on the test set of linear estimator is only **0.1752** when $L_{out}=720$, which is much smaller than the MSE of backbone model (0.498), meaning that the estimator can well assess the quality of individual forecasting results. Similar conclusions can be drawn from the case illustration in Fig3 in our paper, where the estimated and actual error curves exhibit consistent patterns in terms of peaks and troughs.\n\n  | ETTh1/MSE | $L_{in}$=96 |                   |                |\n  | --------- | ----------- | ----------------- | -------------- |\n  |           | PatchTST    | +Linear Estimator | +TRM Estimator |\n  | 96        | 0.410       | 0.375             | 0.374          |\n  | 192       | 0.458       | 0.422             | 0.425          |\n  | 336       | 0.498       | 0.467             | 0.468          |\n  | 720       | 0.498       | 0.484             | 0.490          |\n\n  - Finally, we propose that the lead-lag effects may help to produce accurate results and therefore **the lags are not the key for uncertainty estimation but for the revision process**. Instead of explicitly modeling lead-lag relationships, our local revision component leverages a channel-wise attention mechanism to capture diverse and informative patterns across covariates and exogenous variables. In particular, we incorporate available timestamps to guide the revision process in scenarios with potential distribution shifts—such as those induced by weekdays and holidays—as discussed in Line 234 of the main paper. Further explorations on contextual information modeling are provided in Section 3 of the appendix.\n\nWe hope our responses adequately address your concerns, and we sincerely appreciate the opportunity to clarify and improve our work. We will include the suggested experiments, discussions and in-depth cases in our revised paper."}, {"review_id": "QfFJgzVz7e", "reviewer": "Reviewer_6UsG", "summary": "This paper proposes PIR, a post-hoc refinement method for time series forecasting that improves accuracy through instance-level revision. PIR first identifies potentially erroneous predictions using an auxiliary regressor trained to estimate MAE. Then it revises the initial prediction in two ways: a local revision uses a Transformer to refine the initial forecast based on its own output, and a global revision retrieves relevant instances from the training data to guide correction.", "questions": "1. I want to know what happens if the loss terms are included in the original training process. (W1)\n\n2. Please clarify that uncertainty estimator's prediction really align with the actual error, and its projections do not deteriorate the measured uncertainty. (W3)\n\n3. Please compare with linear baselines (W4)\n\n4. And other miscellaneous paper works (W2, W5)", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1. The high-level idea is promising, and the methodology is relevant and well-aligned with the goal.\n\n2. The paper is clearly written and easy to follow.\n\nWeaknesses\n\n1. It is necessary to verify whether the observed performance gains are simply due to increased model capacity or training time, particularly in the case of the local revision module. What happens if the loss terms are incorporated into the original training process, instead of post-processing?\n\n2. For global revision, the idea of retrieving historical patches and computing a weighted sum is closely related to RAFT. A methodological comparison with RAFT would strengthen the paper.\n\n3. The paper lacks a detailed evaluation of the uncertainty estimator's performance. In addition, unless explicit constraints are applied during projection, the direction of the projection vector may change. This could lead to situations where increasing $\\delta$ results in decreased $\\alpha$ or $\\beta$. If no constraint is enforced in the implementation, experimental validation of this behavior is needed.\n\n4. While the use of strong Transformer-based baselines is appreciated, linear baselines should also be included. DLinear has shown that linear models can perform competitively with Transformers, and RAFT extends this by incorporating retrieval. Including these would provide a more balanced and informative comparison. (RAFT is a very recent work, so while its inclusion would be beneficial, it is also reasonable if it is omitted.)\n\n5. The current qualitative analysis (Figure 3) is useful, but the showcase in Section F (Figure 6) is even more compelling. Including this example in the main paper would make the contribution more impactful.\n\n[1] Retrieval augmented time series forecasting (ICML 2025)\n[2] Are transformers effective for time series forecasting? (AAAI 2023)", "was_revised": true, "final_justification": "After reviewing the authors’ rebuttal and additional experiments, I am increasing my score. The authors addressed key concerns with detailed and well-supported responses:\n\n1) Effectiveness of PIR: Ablation studies show that PIR outperforms simple model scaling and training from scratch, validating its design and two-stage training.\n\n2) Uncertainty estimation: The authors demonstrated strong alignment between estimated and actual errors (e.g., estimation error 0.1752 vs. MSE 0.498), and explained the learned projection behavior clearly.\n\n3) Generality: PIR improves performance across additional models (DLinear, RAFT), confirming its generalizability beyond transformer-based backbones.\n\nOverall, the concerns have been sufficiently addressed, and the contribution is now clearer and stronger.", "rebuttal": "Thank you for your acknowledgement and valuable feedbacks on our work, we would like to address your concerns as follows.\n\n- [Q1] We provide additional comparison experiments as shown below. Here, “**Increase model capacity**” refers to an iTransformer model with comparable parameter count to the PIR-enhanced version, and “**+PIR (scratch)**” denotes the variant where PIR’s loss terms are incorporated from the start without pretraining the forecasting backbone:\n\n  |             |      | iTransformer |       | +PIR  |       | Increase model capacity |       | +PIR(scratch) |       |\n  | ----------- | ---- | ------------ | ----- | ----- | ----- | ----------------------- | ----- | ------------- | ----- |\n  |             |      | MSE          | MAE   | MSE   | MAE   | MSE                     | MAE   | MSE           | MAE   |\n  | Electricity | 96   | 0.148        | 0.240 | 0.145 | 0.237 | 0.147                   | 0.239 | 0.164         | 0.256 |\n  |             | 192  | 0.163        | 0.254 | 0.161 | 0.251 | 0.163                   | 0.255 | 0.178         | 0.270 |\n  |             | 336  | 0.177        | 0.270 | 0.175 | 0.268 | 0.177                   | 0.271 | 0.196         | 0.284 |\n  |             | 720  | 0.227        | 0.311 | 0.219 | 0.303 | 0.217                   | 0.304 | 0.256         | 0.334 |\n  | Weather     | 96   | 0.174        | 0.214 | 0.170 | 0.211 | 0.177                   | 0.218 | 0.217         | 0.249 |\n  |             | 192  | 0.222        | 0.255 | 0.217 | 0.252 | 0.224                   | 0.257 | 0.252         | 0.279 |\n  |             | 336  | 0.281        | 0.299 | 0.277 | 0.298 | 0.279                   | 0.296 | 0.300         | 0.315 |\n  |             | 720  | 0.361        | 0.352 | 0.356 | 0.350 | 0.358                   | 0.350 | 0.393         | 0.371 |\n\n  Benefiting from both global and local revision components, PIR effectively utilizes retrieved similar historical series as well as valuable contextual insights from covariates and exogenous variables. This allows PIR to outperform simply enlarging model capacity. Furthermore, training PIR from scratch leads to degraded performance, possibly because the randomly initialized backbone produces unstable forecasts in early training stages, which negatively affects the optimization of the failure identification module and weakens its ability to estimate forecasting error.\n\n- [Q2] \n\n  - We illustrate the alignment between the uncertainty estimator’s prediction and actual forecasting errors in Fig. 3 of our paper. Here we mistakenly place the suboptimal results on the Weather dataset (compared to the results on the Solar dataset, and we will correct the mistake in the revised paper), yet the estimated and actual error curves exhibit consistent patterns in terms of peaks and troughs, which validates PIR’s capability to assess the quality of individual forecasting results. To be more specific, the estimation error $L_{ue}$, defined in Eq1 in our paper, on the test set of linear estimator is only **0.1752** when $L_{in}=96$,$L_{out}=720$ on the ETTh1 dataset using PatchTST as the backbone model, which is much smaller than the MSE (0.498) of backbone model, demonstrating that the uncertainty estimator's prediction really align with the actual error. \n  - Besides, your concern on the projections is of great value. We do not include explicit constraints on these projections, while the learned results indeed meet the expectations. For example, the weights of $\\alpha$'s projectin learned on the ETTh1 dataset of 4 target lengths are [0.9579, 0.9620, 0.9699, 0.9776] respectively, ensuring a positive correlation between $\\alpha$ and $\\delta$. Since the global revision process considers both estimated uncertainty and retrieved similarity, we do not enforce a simple positive correlation between $\\beta$ and $\\delta$. Instead, we employ an MLP to learn their relationship. As shown in the case study in Fig. 7, the model tends to assign higher $\\beta$ values to samples with higher average similarity, which is consistent with our expectations.\n\n- [Q3&Q4]\n\n  - Our experiments have already included a linear-based forecasting model, SparseTSF, for comparison. Here we also present additional experiments on the traditional DLinear model and the suggested RAFT model as follows. Note that we fix $L_{in}=96$ therefore the results may have differences.\n\n    |       |      | DLinear |       | +PIR  |       | RAFT  |       |\n    | ----- | ---- | ------- | ----- | ----- | ----- | ----- | ----- |\n    |       |      | MSE     | MAE   | MSE   | MAE   | MSE   | MAE   |\n    | ETTm1 | 96   | 0.318   | 0.376 | 0.284 | 0.336 | 0.288 | 0.340 |\n    |       | 192  | 0.427   | 0.441 | 0.366 | 0.389 | 0.384 | 0.401 |\n    |       | 336  | 0.466   | 0.468 | 0.412 | 0.424 | 0.431 | 0.445 |\n    |       | 720  | 0.748   | 0.623 | 0.418 | 0.438 | 0.434 | 0.459 |\n    | Solar | 96   | 0.284   | 0.373 | 0.235 | 0.276 | 0.226 | 0.287 |\n    |       | 192  | 0.315   | 0.393 | 0.277 | 0.299 | 0.251 | 0.311 |\n    |       | 336  | 0.349   | 0.411 | 0.304 | 0.320 | 0.273 | 0.339 |\n    |       | 720  | 0.354   | 0.410 | 0.300 | 0.322 | 0.266 | 0.343 |\n\n    It can be inferred that our PIR demonstrates generalizability on the DLinear model, yielding significant performance improvements. Besides, even compared with the most recent approach, our framework can achieve competitive results.\n\n  - Thank you for pointing out the related work. We will include a detailed discussion of the RAFT method in the revised paper. While RAFT also adopts a retrieval-based strategy—enhancing diversity through multi-period retrieval—it ultimately builds a linear forecasting model. In contrast, our method is not designed to propose a new forecasting architecture. Instead, it is motivated by the observation of instance-level variance and aims to build a general framework that corrects potential prediction failures of backbone models from a post-processing perspective. To this end, we introduce two components: a global retrieval component and a local covariate modeling component. The global retrieval component is conceptually similar to the retrieval module in RAFT. Moreover, we share the same insight as RAFT by employing different strides in the retrieval process to balance between pattern diversity and computational efficiency.\n\nWe hope our responses adequately address your concerns, and we sincerely appreciate the opportunity to clarify and improve our work. We will include the suggested experiments, discussions and in-depth cases in our revised paper."}]

Author rebuttal:

Meta-review: The authors proposed a novel post-training methodology, which is model-agnostic and designed to further enhance forecasting accuracy. The main advantage of this paper is the universal applicability of the proposed method, as it can be integrated with any existing forecasting model. Moreover, the additional results provided during the rebuttal period improve the validity of the proposed framework. One limitation of this study is that the performance improvements are sometimes limited for some forecasting models, especially when considering the additional computational resources required during the post-training phase. In conclusion, the contributions of the paper are clear, and the successful rebuttals have strengthened the authors' claims with more robust supporting evidence.
Decision: Accept (poster)