Tackling Time-Series Forecasting Generalization via Mitigating Concept Drift
Authors: Zhiyuan Zhao
Haoxin Liu
B. Aditya Prakash
Venue: ICLR 2026 Poster (2026)
Keywords: Time-Series Forecasting
Distribution Shift
Concept Drift
Primary area: learning on time series and dynamical systems

Abstract: Time-series forecasting finds broad applications in real-world scenarios. Due to the dynamic nature of time series data, it is important for time-series forecasting models to handle potential distribution shifts over time. In this paper, we initially identify two types of distribution shifts in time series: concept drift and temporal shift. We acknowledge that while existing studies primarily focus on addressing temporal shift issues in time series forecasting, designing proper concept drift methods for time series forecasting has received comparatively less attention.

Motivated by the need to address potential concept drift, while conventional concept drift methods via invariant learning face certain challenges in time-series forecasting, we propose a soft attention mechanism that finds invariant patterns from both lookback and horizon time series. Additionally, we emphasize the critical importance of mitigating temporal shifts as a preliminary to addressing concept drift. In this context, we introduce ShifTS, a method-agnostic framework designed to tackle temporal shift first and then concept drift within a unified approach. Extensive experiments demonstrate the efficacy of ShifTS in consistently enhancing the forecasting accuracy of agnostic models across multiple datasets, and outperforming existing concept drift, temporal shift, and combined baselines.

Published as a conference paper at ICLR 2026
TACKLING TIME-SERIES FORECASTING GENERALIZA- TION VIA MITIGATING CONCEPT DRIFT
Zhiyuan Zhao
Haoxin Liu
Georgia Institute of Technology leozhaol 997 9978gatech edu
Georgia Institute of Technology
h1 i uu7 (17763ggate wrr.egggtcch........ edu
B. Aditya Prakash
Georgia Institute of Technology badityapece. gwtech.eee............. edu
ABSTRACT
Time-series forecasting finds broad applications in real-world scenarios. Due to the dynamic nature of time series data, it is important for time-series forecasting models to handle potential distribution shifts over time. In this paper, we initially identify two types of distribution shifts time series: concept drift and temporal shift. We acknowledge that while existing studies primarily focus on addressing temporal shift issues in time series forecasting, designing proper concept drift methods for time series forecasting has received comparatively less attention.
Motivated by the need to address potential concept drift, while conventional con- cept drift methods via invariant learning face certain challenges in time-series forecasting, we propose a soft attention mechanism that finds invariant patterns from both lookback and horizon time series. Additionally. we emphasize the critical importance of mitigating temporal shifts as a preliminary to addressing concept drift. In this context, we introduce Shi ITS, a methood-agnotti framework designed to tackle temporal shift first and then concept drift within a unified ap- proach. Extensive experiments demonstrate the efficacy of Shi FTS in consistently enhancing the forecasting accuracy of agnostic models across multiple datasets, and outperforming existing concept drift, temporal shift, and combined baselines.
INTRODUCTION
Time-series forecasting finds applications in various real-world scenarios such as economics, urban computing, and epidemiology (Zhu & Shasha 2002|ZZhmg et al. [014 Deb et al.) [017]] Mathis et al.) 2024). These applications involve predicting future trends or events based on historical time-series data. For example, economists use forecasts make financial and marketing plans, while sociologists use them to allocate resources and formulate policies for traffic or disease control.
The recent advent of deep learning has revolutionized time-series forecasting, resulting in series of advanced forecasting models (Lai et al. 2018 Torres et al. 2021: Salinas et al.) (2020] Nie et al. 2023 Zhou et 2.2T). However, despite these successes, time-series lorecasting faces certain challenges from distribution shifts due to the dynamic and complex nature of time series data. The distribution shifts time series can be categorized into two types (Granger 2003). First, the data distributions of the time series data themselves can change over time, including shifts in mean, variance, and autocorrelation structure, which is referred to as non-stationarity or temporal drift issues time-series forecasting (Shimodaira) 2000; Du et al., (021I. Second, time-series forecasting is compounded by unforeseen exogenous factors, which shifts the distribution of target time series. These types of phenomena, categorized as concept drift problems in time-series forecasting (Gama et al. 2014 et al. 2018), make it even more challenging.
While prior research has investigated strategies mitigate temporal shifts (Liu et al. 2022 Kim et al.,
2021 Fan et al. 2023). addressing concept drift issues in time-series forecasting has been largely overlooked. Although concept drift is well-studied problem in general machine learning (Sagawal

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Published as a conference paper at ICLR 2026
et al. 2019: Arjovsky al. 2019 Ahuja al. 2021 adapting these solutions time-series forecasting is challenging. Many these methods require environment labels, which are typically unavailable in time-series datasets (Liu et al., 2024a). Indeed, the few concept drift approaches developed for time-series data are designed exclusively for online settings (Guo et al. 2021), which requires iterative retraining over time steps and is infeasible when applied to standard time-series forecasting tasks.
Therefore, we aim to close this gap in the literature in this paper, that is, mitigate concept drift in time-series forecasting for standard time-series forecasting tasks. The contributions of this paper are:
1. Concept Drift Method:
We introduce soft attention masking (SAM) designed to mitigate concept drift by using the invariant patterns in exogenous features. The soft attention allows the time-series forecasting models weigh and ensemble of invariant patterns multiple horizon time steps to enhance the generalization ability.
2. Distribution Shift Generalized Framework: shift as a preliminary when addressing concept drift. We therefore propose Shi f practical, distribution shift generalized, model-agnostic framework that tackles temporal shift and concept drift within a unified approach.
We show the necessity of addressing temporal
3. Comprehensive Evaluations: We conduct extensive experiments on various time series datasets with multiple advanced time-series forecasting models. The proposed ShifTs fTS demonstrates effectiveness by consistent performance improvements to agnostic forecasting models, well as outperforming distribution shift baselines in better forecasting accuracy.
We provide related works on time-series analysis and distribution shift generalization Appendix
PROBLEM FORMULATION
2.1 TIME-SERIES FORECASTING
Time-series forecasting involves predicting future values one or more dependent time series based on historical data, augmented with exogenous covariate features. Let denote the target time series as Y and its associated exogenous covariate features as X. At any time step t, time-series forecasting aims to predict Y = [yt + 1, 3t.22...... M++H]] E Y using historical data (X,', Y! where L represents the length of the historical data window, known the lookback window, and H denotes the forecasting time steps, known the horizon window. Here, X [24-L+1: -t- L-+2s ,.,, xz) X and Y L+1, Vt- - -+2.------ ye] Y. For simplicity, we denote Y (Y() for Vt as the collection of horizon time-series of all time steps, and similar for Y and xL_ Conventional time- series forecasting involves learning model parameterized by 0 through empirical risk minimization (ERM) to obtain fa (X", Y²) - " for all time steps f. In this study, we focus on univariate time-series forecasting with exogenous features, where dy 1 and dx
2.2 DISTRIBUTION SHIFT IN TIME SERIES
Given the time-series forecasting setups, a time-series forecasting model aims to predict the target distribution P(Y = P( ( + P(Y " (x) which should be generalizable for both training and testing time steps. However, due to the dynamic nature of time-series data, forecasting faces challenges from distribution shifts, categorized into two types: temporal shift and concept drift. These two types of distribution shifts are defined follows:
Definition 2.1 (Temporal Shift (Shimodaira, 2000; Du et al. (021)) Temporal shift (also known as virtual shift (Tsymball 2004)) refers phenomenon that the marginal probability distributions change over time, while the conditional distributions are the same.
Definition 2.2 (Concept Drift (Lu al. 2018)) Concept drift (also known as real concept drift (Gama et al. 2014 D is the phenomenon where the conditional distributions change over time, while the marginal probability distributions are the same.
*Gama et al. 2014) defines concept drift as both virtual shift and real concept drift. Our concept drift definition is consistent with the definition of real concept drift in (Gama al. 2014).
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Intuitively, temporal shift indicates unstable marginal distributions (e.g. P(Y P(Y
while concept drift indicates unstable conditional distributions (P(Y, x & P(Y"IXX) for some i E t). Existing methods for distribution shifts in time-series forecasting typically focus on mitigating temporal shifts through normalization, ensuring P(Y P(Y by both normalizing
standard 0-1 distributions (Kim al.. 2021; Liu al. 2022 Fan al. 2023 In contrast, concept
drift remains relatively underexplored in time-series forecasting.
Nevertheless, time-series forecasting does face challenges from concept drift: The correlations between X and Y can change over time, making the conditional distributions P(Y unstable and less predictable. A demonstration visualizing the differences and relationships between temporal shift and concept drift is provided in Appendix
While the concept drift issue has received considerable attention in existing studies on general machine learning, applying them, mostly invariant learning approaches, time-series forecasting tasks presents certain challenges. Firstly, conventional approaches to mitigate concept drift are through invariant learning. However, these invariant learning methods typically rely on explicit environment labels as input (e.g.. labeled rotation or noisy images in image classification), which are not readily available in time series datasets. Second, these invariant learning methods assume that all correlated exogenous features necessary to fully determine the target variable are accessible (Liu al., 2024a), which are often not applied time series datasets (e.g.. lookback window information sufficiently determining the horizon target). Indeed, few concept drift methods not based on invariant learning have been proposed for time-series forecasting (Guo et al. (2021) However, these methods are designed for the online setting which does not fit standard time-series forecasting, and are only validated on limited synthetic datasets rather than complicated real-world ones.
METHODOLOGY
The main idea of our methodology is to address concept drift through SAM by modeling stable conditional distributions on surrogate exogenous features with invariant patterns, rather than the sole lookback window. Furthermore, we recognize that effectively mitigating temporal shifts is preliminary for addressing concept drift. To this end, we propose Shi ETS ShifTS that effectively handles concept drift by first resolving temporal shifts as preliminary step within a unified framework.
3.1 MITIGATING CONCEPT DRIFT
Methodology Intuition. As defined in Definition 2.2 concept drift in time-series refers to the changing correlations between X and Y over time (P(Y"IXX) # P(Y Xx) for j.j E t), which introduces instability when modeling conditional distribution P(y x This instability arises because, for given exoge- nous feature X, its lookback window X alone may lack sufficient information to predict Y while learning stable conditional distribution requires that the inputs provide sufficient informa- tion to predict the output (Sagawa et al., 2019 Ar jovsky et al. 2019). There are possible patterns in the horizon window X joint with x'. that influ- ence the target. Thus, modeling " "1 x x") leads to more stable conditional distribution com- I? captures addi- tional causal relationships across future time steps. We assume that incorporating causal relationships from the horizon window enables more complete causality modeling between that exogenous fea- ture and target, given that the future cannot influ- ence the past (e.g.. x ~ Y!!). However, these causal effects from the horizon window, while im- portant for learning stable conditional distributions, are often overlooked by conventional time-series forecasting methods, illustrated in Tigure]a)
(a) Conventional Time- Series Forecasting
Our Method
Missnn
X
X
X
X-SURR
y
Lookback
Horizon
Lookback
Horizon
Timskns
Timeline
pared to P(Y H X [ x
Figure 1: Comparison between conventional time-series forecasting and our approach. Our approach identifies invariant patterns in lookback and horizon window X SU R and then models a stable conditional distribution accordingly to mitigate concept drift.
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Therefore, propose leveraging both lookback and horizon information from exogenous features (i.e.. Xx x" to predict the target, enabling more stable conditional distribution. However, di- rectly modeling P(Y"IX' x²) in practice presents two challenges. First, X typically represents unknown future values during testing. To model P(Y [x, x²), it may require to first predict X (xx) which can be challenging as predicting Y directly. Second, not every pattern in X ! at every time step holds causal relationship with the target. Modeling all patterns from X and X may introduce noisy causal relationships (as invariant learning methods aim to mitigate) and reduce the stability of conditional distributions.
by modeling P(x #f
To address the above challenges, instead of directly modeling P(Y#I' x we propose two- step approach: first, identifying patterns in [X", X "I that lead to stable conditional distributions (namely invariant patterns), and then modeling these conditional distributions accordingly. To determine stability, natural intuition is to assess whether a pattern's 's correlation with the target remains consistent across all time steps. For instance, if a subsequence of [X' ; .X"] consistently exhibits stable correlations with the target over all or most time steps (e.g., an increase of the subsequence always results in an increase of the target), then its conditional distribution should be explicitly modeled due to the stability. Conversely, if a subsequence demonstrates correlations with the target only sporadically or locally, these correlations are likely spurious, which are unstable conditional distributions to other time steps. We leverage this intuition to identify all invariant patterns and aggregate them into surrogate feature X-SUR accounting for the fact that the target can be determined by multiple patterns. For instance, be triggered by either extreme cold weather in winter or extreme heat waves in summer (Nielsen et al. 2011 Jaakkola et al., 2014). By incorporating this information, model the corresponding conditional distribution P(Y |X SUR), as illustrated in Figure 1b).
influenza-like illness (ILI) outbreak in winter can
The effectiveness of SUR in predicting Y stems from two key insights. First, P(Y H |XSUR) is stable conditional distribution to model, as it captures invariant patterns across both the lookback and horizon windows. Second, while there a trade-off rade-oof-P(Y"" P(Y" X provides stability, but estimating X SUR may introduce additional
evaluations demonstrate that the benefits of constructing stable conditional distributions outweigh the potential estimation errors of X SUR This is because XSUR contains only partial information, which is easier to predict than the entire X=
Methodology Implementation. Recognizing that P(Y SUS is the desirable conditional distri- bution to learn, the remaining challenge is to identify x SSUR in practice. To achieve this, we propose a soft attention masking mechanism (SAM), that operates as follows: First, we concatenate [X4 = to form an entire time series of length L + H. The entire series is then sliced using sliding window of size H, resulting in L + slices. This process extracts local patterns (X L.......... x each time step I), which are subsequently used to identify invariant patterns.
Second, we model the conditional distributions for all local patterns P(y...,,(Y!,"""" P(Y x ] at each time step t, with applying learnable soft atten-
[P(Y H X ....... .,, tion matrix M to weigh each local pattern. This matrix incorporates softmax, sparsity, and normalization operations, which can be mathematically described
Softmax Mj Softmax(M,)
Sparsity:
My Mag 1 1 (MMM))(M2))0 Mj
Normalize: Mj [M,
where i,j are the first and second dimensions of M. These operations are essential for SAM identifying invariant patterns. The intuition is that we consider sliced windows from the lookback and horizon over time steps candidates of invariant patterns. We use the softmax operation to compute and update the weights of each pattern contributing to the target Y We then apply sparsity operation to filter out patterns with low weights, leaving only the patterns with high weights. These high- high-weight patterns, which consistently contribute to the target across all instances at all time steps, are regarded as invariant patterns over time. These patterns intuitively are invariant patterns as P(Y," (x"") xe P "! {x ).) for some & E [0. L) and j.j j E t. While multiple invariant patterns may be identified, compute weighted sum of these patterns, proportional to their contributions
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(a)
(b)
(c)
Exoganous Series
x
Forecant
Aggregetion
Mitigating
Temporal Shift
Attention Mank
Mitigating
X
Denorm
Concept Drift
Nomm
y
Torpet Prodiction
Target Series
Forecant
y!
9"
Figure 2: Diagram of ShifTS, consisting of three components: (a) normalization the start (c) denormalization at the end to address temporal shifts, and (b) a two-stage forecasting process- The first stage predicts surrogate exogenous features, SURR, identified by the SAM, which capture invariant patterns essential for forecasting the target; The second stage uses both the predicted surrogate exogenous features and the original Y to predict Y
in predicting the target. The weighted-sit sum patterns formulate the surrogate feature X SUR For simplicity, we denote this process as:
SUR -SAM x
Σ M(Slice([** xxx x))))
where Slice(-) represents slicing the time series IL + H. dxl HH 11.L+1,xx/ dx]. and M Rl+1xxx is the learnable soft attention as in Equation |I
In practice, X SUR may include horizon information unavailable during testing. To address this, SAM estimates the surrogate features X SUR using agnostic forecasting models. The surrogate loss that aims to estimate SUUR is defined as:
SSR MSE(X SUR SUR)
3.2 MITIGATING TEMPORAL SHIFT
While the primary contribution of this work is to mitigate concept drift in time-series forecasting, addressing temporal shifts is equally critical and serves prerequisite for effectively managing concept drift. The key intuition is that SAM seeks to learn invariant patterns that result in a stable conditional distribution, P(Y" !1 XSRR. However, achieving this stability becomes challenging if the marginal distributions (e.g., P(Y ) or P(XSUR)) are not fixed, as these distributions may change over time because of the temporal shift issues.
To address this issue, a natural solution is to learn the conditional distribution under standardized marginal distributions. This be achieved using temporal shift methods, which employ instance normalization techniques to stabilize the marginals. The core intuition behind popular temporal shift methods is normalize data distributions before the model processes them and denormalize the outputs afterward. This approach ensures that the normalized sequences maintain consistent mean and variance between the inputs and outputs of the forecasting model. Specifically, (( R (0, 1), thereby mitigating temporal
P ) ~ (Ost(0, 1) and k Norm R P( shifts (i.e., shifts in marginal distributions over time).
Among the existing methods, Reversible Instance Normalization (RevIN) (Kim et al. 2021) stands out for its simplicity and effectiveness, making it the method choice in this work. Advanced techniques, such as SAN (Liu et al.) (203) and N-S Transformer (Liu et al. 2022). have also demonstrated promise in addressing temporal shifts. However, these methods often require modifications to forecasting models additional pre-training strategies. While exploring these advanced temporal shift approaches remains a promising avenue for further performance improvements, it beyond the scope of this study and not the primary focus of this work.
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3.3 SHIFTS: THE INTEGRATED FRAMEWORK
To address concept drift in time-series forecasting, while acknowledging that mitigating temporal shifts is prerequisite for resolving concept drift, propose ShiffS comprehensive framework designed to tackle both challenges in time-series forecasting. Shi FTS model-agnostic, as the stable conditional distributions distinguished by SAM can be learned by any time-series, forecasting model. The workflow of Shiff thifTSI is illustrated in Figure 2 and consists of the following steps: (1) Normalize the input time series; (2) Forecast surrogate exogenous features S that invariantly support the target series, determined by SAM; (3) An aggregation MIP that uses XSUR to forecast the target, denoted as Agg(-) in F Algorithm [ (4) Denormalize the output time series. Conceptually, steps 1 and 4 mitigate the temporal shift, step 2 addresses concept drift, and step performs weighted aggregation of exogenous features to support the target series. The optimization
objective of Shi FTS is as follows:
L LSUR (X XUU LIs Y
Here, LSUR is the surrogate loss that encourages learning to forecast exogenous features, and LTs is the MSE loss used in conventional time-series forecasting, The pseudo-code for training and testing Shi FTS is provided in Algorithm
Algorithm 1 ShifTS
I: Training: Require: Training data X², x YL, H Initial parameters fo. Mo. Aggo:
Output: Model parameter f. .M, Agg
2: For i in range (E):
3: Normalization:
Norm = Norm (X., Y
I
Norm
4: Time-series forecasting:
X
SUR
Norm!
Norml = K
Norm
Norml)
5: Exogenous feature aggregation:
H
Norm + AgK,
SUR
Norm
Norm
6:
Denormalization:
SUR
YH Denorm (X
SUR
H
Norm
Norm
7: Obtain sufficient ex ex-features:
X SUR SAM x "1
8: Compute loss:
L = (XUR(X** SUR XSUR) LTS Y Y
9: Update model parameter:
fit1 t fú, Mr+1 + Mr Aggi+1 Agg,
10: Final model parameters: f + SE. M +- ME, Agg t Agg
11:
Testing: Require: Test data XL, Y Output: Forecast target Y
12:
Normalization:
X Norm SUR Norm
Y L
Norm! N &
Y'D
13:
Time-series forecasting:
Norm = s[X
Norm: Y Korm))
14:
Exogenous feature aggregation:
YH
Norm Agg (XSUR
Norm SUR
15:
Denormalization:
&
Denorm Norm
SUR
SUR
Y Norm
4 EXPERIMENTS
4.1 SETUP
Datasets. We conduct experiments using six time-series datasets leveraged in (Liu et al. 2024a):
The daily reported currency exchange rates (Exchange) (Lai et al. [2018;; The weekly reported influenza-like illness patients (IL.I (Kamarthi et al., 202T): Two-hourly/minueely reported electricity transformer temperature (ETTh 1/ETTh2 and (TTmm/ETTml respectively) (Zhou et al., 2021). We follow the established experimental setups and target variable selections in previous works Wu et al. 2021 2022, Nie et al.) 2023 Liu et al. (2024d). Datasets such Traffic (PeMS) (Zhao et al. 2017 and Weather (Wu et al. 2021) are excluded from our evaluations, as their time series exhibit near-stationary behavior, with only moderate distribution shift issues. Further details on the dataset differences are discussed in Appendix C.I
Baselines. We include two types of baselines for comprehensive evaluation Shi OTS:
Forecasting Model Baselines: ShifTS is model-agnostic, we include six time-series forecast- ing models (referred to as 'Model" in Table T and 4), including: Informer (Zhou et al. 2021)

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Table 1: Performance comparison on forecasting errors without (ERM) and with Shi FTS. Employing
Shi FTS shows consistent performance gains agnostic to forecasting models. The top-performing method is in bold. 'IMP. denotes the average improvements over all horizons of Shi FTS vs ERM.
Model
Crossformer (ICLR'23)
PT
(CCL)233)
iTranstormer (ICLR 24)
Method
FRM
Shi FTS
FRM
FTS
FRM
Sh1
FTS
Dataset
MSE
MAE
MSE
MAE
MSB
MAE
MSB
MAE
MSE
MAE
MSE
MAE
24
3.409
1.604
0.674
0.590
0.772
0.634
0.656
0.618
0.824
0.653
0.799
0.642
36
4.001
1.772
0.687
0.617
0.763
0.649
0.694
0.602
0.917
0.738
0.690
0.640
ILI
48
3.720
1.724
0.652
0.611
0.753
0.692
0.654
0.630
0.772
0.699
0.680
0.665
60
3.689
1.715
0.658
0.633
0.761
0.724
0.680
0.656
0.729
0.710
0.672
0.667
IMP.
81.9%
64.0%
12.0%
7.1%
13.8%
6.5%
96
0,338
0.475
0.102
0.237
0,130
0.265
0.102
0.236
0.135
0.272
0.115
0.255
Exchange
192
0,566
0.622
0.203
0.338
0.247
0,394
0.194
0.332
0.250
0.376
0,209
0.343
336
1.078
0.867
0.407
0.484
0.522
0.557
0,388
0.477
0.450
0.503
0.426
0.495
720
1.292
0,963
1.165
0,813
1.171
0.824
0.995
0.747
1,501
0.941
1.138
0.827
IMP.
53.5% %
38.9%
20.9%
12.6%
15.2%
6.9%
96
0.145
0,312
0.055
0,180
0.064
0.193
0,056
0.181
0.061
0.190
0.056
0.181
E
192
0.240
0.420
0.072
0,206
0.085
0.222
0.073
0.209
0.076
0.219
0.072
0.205
336
0.240
0,424
0.084
0.228
0.096
0,244
0.089
0.235
0.086
0.227
0.083
0.225
720
0.391
0,553
0.095
0.244
0.128
0,282
0,097
0.245
0,085
0.232
0,082
0.230
IMP.
68.2%
48.8%
14,5%
7.2%
5.1 %,1%
3.3%
96
0.255
0.408
0.137
0,286
0.154
0.309
0.139
0.287
0.141
0.292
0.137
0.288
B
192
1.257
1.034
0.182
0.338
U.204
0.374
0,191
0.345
0.194
0.347
0.184
0.339
336
0.783
0,771
0.234
0,388
0.252
0.406
0.222
0.381
0.229
0.383
0.225
0,381
720
1.455
1.100
0.234
0.389
0.259
0.411
0.236
0.390
0.266
0.413
0.235
0,390
IMP.
71.4%
52.9%
9.2%
6.5%
5.4%
2.5%
96
0.050
0.174
0.028
0.126
0.031
0.135
0.029
0.128
0.030
0.131
0.030
0.131
ET1m2 E17ml
192
0,271
0.454
0.043
0.158
0.048
0.166
0.044
0.161
0,049
0.171
0.046
0.165
336
0.731
0.805
0.057
0.184
0.058
0.190
0.058
0.186
0.066
0.199
0.059
0.188
720
0.829
0.849
0.083
0.219
0.083
0,223
0,080
0.219
0.082
0.219
0.079
0.217
IMP.
77.3%
61.0%
4.6%
3.0 %
5.1%
2.5%
96
0.153
0.315
0.069
0.190
0.078
0.206
0.067
0.188
0.073
0.200
0.073
0.195
192
0.408
0.526
0.105
0,242
0.113
0.246
0.101
0.237
0.1
0.251
0.108
0,248
336
0.428
0.504
0.146
0.289
0.176
0.320
0,134
0.278
0.157
0.302
0.144
0.291
720
1.965
1,205
0.191
0.342
0.220
0.368
0,185
0.334
0.196
0.347
0.193
0.344
IMP.
71.3%
52.0%
15.9%
8.6
4.8%
2.1%
Pyraformer (Liu et al. 2021 Crossformer (Zhngg & Yan 2022). PatchTST (Nie et al., 2023).
TimeMixer (Wang et al. 2024) and iTransformer (Liu et al. 2024d), which of the last two are the -tate-of-the--o art (SOTA) forecasting model. These models are used to demonstrate that Shi fTS consistently enhances forecasting accuracy across various models, including SOTA.
Distribution Shift Baselines: We compare ShiFTS with various distribution shift methods (referred to as 'Method' in Ta (1) Three non-stationary methods for addressing temporal distribution shifts in time-series forecasting N-S Trans. (Liu et al. 2022). RevIN (Kim et al. 2021). and SAN (Liu al. 2023). We omit Dish-TS (Fan et al. (002)) and SIN (Han et al. 2024) from the main text due to their instability on univariate targets. (2) Four concept drift methods, including GroupDRO (Sagawa) cet al. 2019), IRM (Arjovsky et al. 2019). VREx (Krueger et al., 202T), and EIIL (Creager et al. 2021). which are primarily designed for general applications. (3) Three combined methods for both temporal distribution shifts and concept drift: IRM+ReNIN, EeI++RevI, and SOTA time-series distribution shift method FOIL (Liu et al. 2024a). These comparisons aim to highlight the advantages of HTS in distribution shift generalization over existing distribution shift approaches.
Evaluation. We measure the forecasting errors using mean squared error (MSE) and mean absolute error (MAE). The formula of the metrics are: MSE- J, > (y - 0² and MAE _ Σ g 9)
Reproducibility. All models are trained on NVIDIA Tesla V100 32GB GPUs. All training data and code are available at: htttp::://// http:://gitttbbb
tyalab/ Shi FTS More experiment details
are presented in Appendix C.2
4.2 PERFORMANCE IMPROVEMENT ACROSS BASE FORECASTING MODELS
To evaluate the effectiveness of ShiFTS in reducing forecasting errors, we conduct experiments comparing performance with and without Shi FTS across popular time-series datasets and four
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Table Averaged performance comparison between ShifTS and distribution shift baselines with Crossformer. Sh FTS achieves the best and second-best performance in 6 and 2 out of 8 evaluations. The best results are highlighted in bold and the second-bes, results are underlined.
Dataset
ILI
Exchange
ETTh1
ETTh2
Method
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
Base
ERM
3.705
1.704
0.819
0.732
0.254
0.427
0.937
0.828
GroupDRO
2.285
1.287
0.821
0.751
0.278
0.453
1.150
0,936
Concept
IRM
2.248
1.237
0.846
0.754
0.201
0.367
0.878
0.792
Drift
VREx
2.285
1.286
0.821
0.742
0.314
0.486
1.142
0,938
Method
EIIL
2.036
1.159
0.822
0.749
0.212
0.433
1.122
0.930
Temporal
RevIN
0.815
0.708
0.475
0.476
0,085
0.224
0.205
0.358
Shift
N-S Trans.
0.781
0.688
0,484
0,481
0.086
0.226
0.203
0.355
Method
SAN
0.757
0.715
0.415
0.453
0.088
0.225
0,199
0,348
IRM+RevIN
0.809
0.711
0,481
0.476
0,089
0.231
0.202
0.362
Combined
ReIL+
0.799
0.706
0.483
0.485
0.085
0.225
0.218
0.380
Method
FOIL
0.735
0.651
0.497
0.481
0.081
0.219
0.206
0.357
ShifTS (Ours)
0.668
0.613
0.470
0.468
0.076
0.214
0.194
0.348
different forecasting horizons. These experiments utilize five transformer-based models and one MLP-based model. Evaluation results for Crossformer, PatchTST, and iTransformer are presented in Table I] while additional results for older models, including Informer, Pyraformer, and TimeMixer, are provided in Table Appendix D.I
The experimental results consistently demonstrate the effectiveness of ShifTS in improving fore- casting performance across agnostic forecasting models. Notably, Shi FTS achieves reductions in forecasting errors of up to 15% when integrated with advanced models like iTransformer. Further- more, Shi FTS shows even greater relative effectiveness when applied to older or less advanced forecasting models, such as Informer and Crossformer.
In addition the observed performance improvements, our results reveal two further insights:
The effectiveness of ShifTS relies on the insights provided by the horizon data. The performance improvements exhibit variations across different datasets. For instance, the application of Shi fTS on ILI and Exchange datasets yields greater performance improvements compared to ETT datasets over- all. To interpret the phenomenon and determine the conditions under which ShifTS could be most effective in practical scenarios, we quantify the mutual information I[x"; YY" shared between X" and Y (detailed setup provided in Appendix C.2 We plot the relationship between I(X"; " Y") and performance gains in Figure ((a) The scatter plot illustrates a positive linear correlation between I(x H. ) and performance gains, supported by a p-value p = 0.012 < 0.05. This observation suggests that the greater the amount of useful information from exogenous features within the hori- zon window, the more substantial the performance gains achieved by Sh i fTS. This insight aligns with the design of Shi FTS, as higher mutual information indicates clearer correlations and causal relationships between the target Y and exogenous features in the horizon often overlooked by conventional time-series models. Stronger correlations imply a greater extent of misrepresented dependencies in ERM, leading to more significant improvements with ShifTS.
The extent of quantitative performance gains achieved by ShifTS depends on the underlying forecasting model. Notably, the extent performance enhancements achieved by Shi FTS varies across different forecasting models. For example, the performance gains on the simpler Informer model by Shi FTS is more significant than the SOTA iTransformer model. Importantly, we emphasize two key observations: Firstly, even when applied to the i'Transformer model, Sh i FTS demonstrates a notable performance boost of approximately 15% on both ILI and Exchange datasets, consistent with the aforehead intuition. Secondly, integrating Shi FTS into forecasting processes should, the very least, maintain or improve the performance of standalone forecasting models, as evidenced by consistent performance enhancements observed across all datasets with iTransformer model.
4.3 COMPARISON WITH DISTRIBUTION SHIFT METHODS
To illustrate the advantages of ShifTS over other model-agnostic approaches for addressing distri- bution shifts, we perform experiments comparing its performance against distribution shift baselines,
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0.50
0.3
0.30
633
Perfomence
0.2
0.15
BIUI
622
0,107
9.33
6437
0.100
R222
8.229
0.1
6.
2.03
3.8
4.5
0.5
055
Information Shared
Figure 3: Left (a): The performance gains of Sh FTS versus the mutual information shared between X and Y Greater mutual information in X compared Y correlates with more significant performance gains achieved by ShiFTS. Right (b): Ablation Study. Addressing either concept drift temporal shift individually provides certain benefits in forecasting accuracy, Sh FTS that tackles both achieves the lowest forecasting emror.
including methods designed for concept drift, temporal shift, and combined approaches. We exclude evaluations minutely ETT datasets, following (Liu et al. 2024a), their data characteristies and forecasting performance closely resemble those of hourly ETT datasets. The experiments utilize Crossformer the forecasting model, and the averaged results are presented in Table
The results highlight the advantages of ShifTS over existing distribution shift methods, achiev- ing the highest average forecasting accuracy in 6 of 8 evaluations, with the remain- ing 2 evaluations ranking second. Notably, as discussed in Section 3.2 we choose to use RevIN as is one of the most popular yet simple and effective temporal shift methods. However, ShifTS is flexible and can inte- grate more advanced temporal shift meth- ods to further enhance performance. While exploring these advanced temporal shift methods is beyond the scope of this work, we illustrate potential benefits of such integration. For example, the Exchange dataset, where SAN outperforms Shi FTS, incorporating SAN in place of RevIN within Shi ETS leads to even greater accu- racy improvements. Detailed MSE values for these evaluations are provided in Table Furthermore, the results underscore the importance of addressing concept drift using SAM when temporal shifts are effectively addressed.
Table 3: MSE comparison between Shi ChifTS, SAN, and Shi fTS+SAN on Exchange dataset. Shi FTS+SAN achieves the best performance all evaluations.
Horizon
ShitTs
SAN
Shi STS W. SAN
96
0.102
0.091
0,089
192
0,207
0.195
0.187
336
0.407
0.373
0.372
720
1.165
1.001
0.981
Avg.
0.470
0.415
0.407
4.4 ABLATION STUDY
To demonstrate the effectiveness of each module in ShifTs we conducted an ablation study using two modified versions: ShifTs fis TS and Shi ChifTs'CCD. Shi ETS).T TS excludes the temporal shift adjustment via RevIN, while Shifrs CD excludes the concept drift handling via SAM. Additionally, conventional forecasting models that do not address either concept drift or temporal shift are denoted as 'Base". We performed experiments on the Exchange datasets using the previous three baseline forecasting models, with fixed forecasting horizon of 96. The results visualized in Figure 3(b) The visualization reveals the following observations:
First, addressing temporal shift and concept drift together, implemented in Shi ETS, yields lower forecasting errors than addressing only one type of distribution shift (ShifTsY and Shi FTS (TS) CD)) not considering any distribution shift adjustments (Base). This suggests that temporal shift and concept drift are interrelated and co-exist in time series data, and addressing both provides significant benefits. Second, for forecasting models that inherently address temporal shift, such PatchTST and

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iTransformer that incorporate norm/denorm, the performance gains from mitigating concept drift more significant than those from additionally mitigating temporal shift using RevIN. In contrast, for models without any temporal shift mitigation, such Crossformer, tackling temporal shift leads to a greater performance improvement than concept drift. These observations suggest that mitigating temporal shift is necessity in mitigating concept drift, which matches the intuition in Section 3.2
CONCLUSION AND LIMITATION DISCUSSION
In this paper, we identify the challenges posed by both concept drift and temporal shift in time-series forecasting. While the issue of mitigating temporal shifts has garnered significant attention within the time-series forecasting community, concept drift has remained largely overlooked. To bridge this gap. we propose SAM, method designed effectively address concept drift in time-series forecasting by modeling conditional distributions through surrogate exogenous features. Building on SAM, we introduce i FTS, model-agnostic framework that handles concept drift in practice by first mitigating temporal shift as preliminary step. Our comprehensive evaluations highlight the effectiveness of Shi FTS, while the benefits of SAM are further demonstrated through an ablation study. We discuss the limitations of our approach in Appendix D
LCKNOWLEDGMENT
This work was partly supported by the NSF (Expeditions CCF-1918770, CAREER ISS-2028566, Medium IIS- 195588,, Medium IIS-2403240, Medium IIS-2106961), NIH (IR01HL184119), CDC MInD program, Meta, and Dolby faculty gifts.
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A RELATED WORKS
Time-Series Forecasting, Recent works in deep learning have achieved notable achievements in time-
series forecasting, such as RNNs, LSTNet, N-BEATS (Sherstinsky) 2020 Lai et al. [0188] Oreshkin
et al. 2020). State-of-the-art models build upon the successes of self-attention mechanisms (Vaswani
et al. 2017) with transformer-basee
architectures and significantly improve forecasting accuracy.
such Informer, Autoformer, Fedformer, PStchTST. iTransformer, FRNet (Zhou et al. 2021; Wu
et al. 202T Zhou et al. 2022 Nic et al., [023 Liu et al. 2024d Zhang et al. 2024| Zhao et al.
2025c). However, these advanced models primarily rely on empirical risk minimization (ERM) with IID assumptions, i.e., train and test dataset follows the same data distribution, which exhibits
limitations when potential distribution shifts time series (Zhao et al. 2025b).
Distribution Shift in Time-Series Forecasting. In recent decades, learning under non-stationary distributions, where the target distribution over instances changes with time, has attracted attention within learning theory (Kuh et al.) 1990, Bartlett 1992). In the context of time series, the distribution shift can be categorized into concept drift and temporal shifts.
General concept drift methods (via invariant learning) (Arjovsky et al. 2019; Ahuja et al. 202 Krueger et al., 2021] Pezeshki et al., 2021, Sagawa et al. 2019) assume instances sampled from various environments and propose to identify and utilize invariant predictors across these environments. However, when applied to time-series forecasting, these methods encounter limitations. Additional methods specifically tailored for time series data also encounter certain constraints: DIVERSITY (Lu et al. 2023) is designed for time series classification and detection only. OneNet (Wen et al. 2024 is tailored solely for online forecasting scenarios using online ensembling. PeTS (Zhao et al. focuses on distribution shifts induced by the specific phenomenon of performativity.
2025a)
Other works explicitly address temporal distribution shift in time-series forecasting (Kim et al. 202 Liu et al.) 2022; Fan et al. 2023 Liu et al.] (003)). These methods typically design normal izztion schemes that align the statistical properties of the lookback and forecast horizon, ensuring that both segments follow comparable normalized distributions. Such alignment mitigates temporal shift arising from discrepancies between historical observations and future targets. More recent time-series foundation models Aksu et al.) (2024); Woo et al. (2024); Daa et al. (2024): [Lu et al.) (2025b); Ansari ct al. (2025) improve generalization by scaling model capacity and training on large and diverse corpora. Through large-scale pretraining and parameter scaling, these approaches may implicitly enhance robustness to distribution shift. However, most existing foundation models focus primarily on univariate settings and do not explicitly leverage rich exogenous information. In parallel, several recent studies (Liu et al., 2024b]c] c Liu et al. 2022aa] 2026) incorporate auxiliary textual context to assist time-series understanding and forecasting. These approaches extend beyond purely numerical modeling and explore multimodal conditioning, which is orthogonal to the scope of this work.
B TEMPORAL SHIFT AND CONCEPT DRIFT
To highlight the differences between concept drift and temporal shift, we provide visualizations of both phenomena. Figure 4 illustrates temporal shift, while Figure demonstrates concept drif
Figures adapted from: https: //gi whg.. com htom/ts-a wti.ttskkiii/eee wwwp///eivlllll Rev
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Temporal shift refers changes in the statistical properties of a univariate time series data, such as mean, variance, and autocorrelation structures, over time. For instance, the mean and variance of the given time series shift between the lookback window and horizon window, depicted in Figure 4 This issue is inherent in time series forecasting and can occur on any given time series data, regardless of whether the data pertains to the target series exogenous features.
In contrast, concept drift describes to changes in the correlations between exogenous features and the target series over time. Figure 5 illustrates this phenomenon, where increases exogenous features at earlier time steps lead to increases in the target series, while increases at later time steps result in decreases. Unlike temporal shift, concept drift involves multiple correlated time series and an inherent issue in univariate time series analysis.
DET
2010.01.11
2010.10.3 10.25
2011
2011.08.0
08
2012.05.23
2013
2018
03.12
2013
12.23
2014.10.08
2015
04.29
2016 02.11
2016.088
2016.08.30
2017 06.15
Temporal Shift:
Mean/Varianee largely varies
Figure 4:
Demonstration of temporal shift phenomenon within time series data, showcasing the varia- tions in statistical properties, including mean and variance, over time as the emergence of temporal shift (Red: ground truth; Yellow: N-BEATS prediction; Blue: N-BEATS+RevIN prediction).
Close
x increases
X increases
y Increases
y decreases
Concept Drift: Variant Correlations
Y
DE1
2010.0111
2010
2011 09.09
2012.5.223
201303112
20.4
09.29
2015.2.111
2016 30
2017 86.5
2013
2014
2015
Figure Demonstration concept drift phenomenon within time series data, showcasing the variations in correlation structures between target series Y and exogenous feature X over time as the emergence of concept drift (Red: ground truth; Yellow: N-BEATS prediction; Blue: N- BEATS+RevIN prediction).
C ADDITIONAL EXPERIMENT DETAILS
C.1 DATASETS
We conduct experiments on six real-world datasets, which are commonly used as benchmark datasets:
ILL. The ILI dataset collects data on influenza-like illness patients weekly, with eight variables.
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Exchange. The Exchange dataset records the daily exchange rate of eight currencies.
ETT. The ETT dataset contains four sub-datasets: ETThI, ETTh2, ETTm1, ETTm2. The datasets record electricity transformer temperatures from two separate counties in China (distinguished by and '2"), with two granularities: minutely and hourly (distinguished by 'm' and 'h'). All sub-datasets have seven variables/features.
We follow (Wu et al. 2022 Nie al. 2023 Liu al., 2024d) to preprocess data, which guides splitting datasets into train/ fain/validan validation/test sets and selecting the target variables. All datasets are preprocessed using the zero-mean normalization method.
Additional popular time-series datasets, such as Traffic (which records road occupancy rates from various sensors San Francisco freeways), Electricity (which tracks hourly electricity consumption for 321 customers), and Weather (which collects 21 meteorological indicators in Germany, such as humidity and air temperature), omitted from evaluations. These datasets exhibit strong periodic signals and display near-stationary properties, making distribution shift issues less prevalent. visualization comparison between the ETThl and Traffic datasets, shown in Figure 6 further supports this observation.
(a)
(b)
X
500-
Sorms
3.04
100
Figure 6: Distribution shift issues across datasets: Left (a): ETT. Both temporal shift and concept drift are present. The target series shows varying statistics over time (c.g., lower variance in earlier periods and higher variance later), causing temporal shift. The correlation between X and Y is unclear and unstable, causing concept drift. Right (h): Traffic. Both temporal shift and concept drift are moderate. The target series exhibits near pear-periodiiity, making the temporal shift moderate. Moreover, the correlation between X and Y remains stable (e.g., both increase or decrease simultaneously). making concept drift moderate.
C.2 BASELINE IMPLEMENTATION
We follow the commonly adopted setup for defining the forecasting horizon window length, as outlined in prior works (Wu et al. 2022, Nie et al., 2023 Liu et al.) 2024d). Specifically, for datasets such as ETT and Exchange, the forecasting horizon windows are chosen from the set [96, 192, 336, 720], with fixed lookback window size of 96 and consistent label window size of 48 for the decoder (if required). Similarly, for the weekly reported ILI dataset, we employ forecasting horizon windows from [24, 36, 48, 60], with fixed lookback window size of 36 and constant label window size of 18 for the decoder (if required).
In the context of concept drift baselines, several baselines like GroupDRO, IRM, and VREx require environment labels, which are typically absent in time series datasets. To address this, we partition the training set into lt equah- time segments to serve as predefined environment labels.
For baseline time-series forecasting models, we follow implementations and suggested hyperparam- eters (with additional tuning) sourced from the Time Series Library3] For concept drift baselines. we utilize implementations and hyperparameter tuning strategies recommended by DomainBed" For temporal shift baselines, we adopt implementations and hyperparameter configurations outlined
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Published as a conference paper at ICLR 2026
in their respective papers. Additionally, add an additional MLP layer to the end PatchTST to effectively utilize exogenous features, following (Liu et al. 2024a).
In the ablation study, for the implementation of PatchIST and iTransformer, follow the original approach by applying norm and denorm operations to the 'Base' model. To clarify our notation, Shi FTS'TS refers to the model with standard norm/denorm operations and SAM, while Shi Shi FTS denotes the version where the regular norm/denorm is replaced with RevIN.
C.3 MUTUAL INFORMATION VISUALIZATION
For given time series dataset, we compute the mutual information I(X#; "xx:Y's YY for each training time step and each exogenous feature dimension individually, following:
P(z.0) v)
I(X "1 "x" x Σ Σ
P(a, log P(z)
(5)
ZEX DEY"
We then average the mutual information across all time steps for each exogenous feature dimension and identify the maximum averaged mutual information allows us to assess the information content cach feature dimension relation to the target series.
all feature dimensions. This process
We visualize the maximum averaged mutual information plotted against the corresponding perfor- mance gain in Figure 3(a) This visualization provides insights into how the information content of different feature dimensions relates to the performance improvement achieved in the forecasting model.
D ADDITIONAL RESULTS
D.1 EVALUATIONS ON AGNOSTIC PERFORMANCE GAINS
To further demonstrate the benefit of fhi in improving the forecasting accuracy over agnostic forecasting models, we additionally evaluate the performance differences without and with ShifTS on Informer, Pyraformer, and MixeMixer. The detailed results are presented in Table The additional evaluations again show consistent performance improvements in these models. Moreover, compared to the results in Table the performance gains on these older models are even more significant. This observation highlights the need to mitigate both concept drift and temporal shift in time-series forecasting, as such problem are rarely considered these models, but the later models (e.g.. PatchTST and i'Transfrmer are compounded with nommalizaioom/deeommaizzzzz processes).
E LIMITATION DISCUSSION
This work introduces SAM to address concept drift and proposes an integrated framework, Shi ETS, which combines SAM with temporal shift mitigation techniques to enhance the accuracy time-scries forecasting. Extensive empirical evaluations support the effectiveness of these methods. However, the limitations of this study lie in two aspects: First, the distribution shift methods in time-series forecasting, including Shi i FTS, lack theoretical guarantee. For example, analysis quantifies how much the error bound can be tightened by addressing concept drift or temporal shift compared to vanilla time-series forecasting methods. Second, while this paper defines concept drift and temporal shift issues within the context of time-series forecasting, SAM and Shi FTS S are not the only possible solutions. Exploring alternative approaches remains an avenue for future research beyond the scope of this work. These two limitations highlight opportunities for future investigation.
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Published as a conference paper at ICLR 2026
Table 4: Performance comparison on forecasting errors without (ERM) and with Shi FTS on Informer, Pyraformer, and TimeMixer. Employing Shi FTS again shows near-consistent performance gains agnostic to forecasting models. The top-performing method is in bold. 'IMP.' denotes the average improvements all horizons of Shi fTS ERM.
Model
Informer (AAAI21)
Pyraformer (ICLR'2)
TimeMixer (ICLR'24)
Method
ERM
ShiFTS
ERM
ShiFTS
ERM
Shi FTS
5.032
1,935
I,030
0.812
4,692
1.898
0.979
0.749
0.853
0.733
0,789
0.702
36
4.475
1.876
1.046
0.850
4.814
1.950
0.866
0.740
0.721
0.676
0.697
0.665
IIJI
48
4.506
1.879
0.918
0.818
4.109
1.801
0.789
0.732
0.737
0.692
0.741
0.711
4.313
1.850
0.957
0.839
4,483
1.850
0.723
0.659
IMP.
78.4%
56.0%
81.5%
61.1%
6.3%
3.0%
96
0.839
0.746
0.137
0.277
0.410
0.525
0.145
0.275
0.127
0.268
0.098
0.234
Exchange
192
0.862
0.773
0.210
0.346
0.529
0.610
0.300
0.404
0.229
0.355
0.214
0.352
336
1.597
1.063
0,378
0.485
0,851
0.778
0,440
0,506
0.553
0,560
0.440
0.491
4.358
1.935
0.760
0.655
1.558
1.067
1,509
0.963
1.173
0.834
0.962
0.747
IMP.
79.5%
59.7%
39.8%
31.5%
16.9%
9.1%
96
0.891
11,663
0.095
0,231
0.653
0.748
0.065
0.197
0.059
0.184
0.059
01187
ETTh1
1.027
0.958
0.096
0.237
0.853
0.828
0.075
0.210
0.099
0.247
0.077
0.211
0.961
0.237
0.238
0.279
0.246
720
1.077
0.969
0.100
0.252
0.562
0.695
0.126
0.279
0.139
0.299
0.099
0.252
IMP.
90.7%
74.5%
86.4
69.6%
23.3%
10.1 %
96
3.195
1.651
0,232
0.381
1.398
1.127
0.156
0,307
0.152
0,303
0.146
0.299
ETTh2
1.778
0.464
0.367
0.349
0.185
0.343
336
2.556
1.468
0.400
0.512
2.571
1.489
0.245
0.398
0.238
0.392
0.230
0.381
720
2.723
1.532
0.489
0.579
2.294
1.409
0.261
0.410
0.273
0.421
0.249
0.397
IMP
82.0%
69.5%
73.5%
5.3%
2.9%
0.433
0.130
0.128
ETTml
192
0.459
0.582
0.079
0.211
0.240
0.4112
0.045
0.162
0.047
0.165
0.047
0.164
336
0.457
0.556
0.104
0.243
0.359
0,512
0.062
0.192
0.063
0.191
0.060
0.189
720
0.735
0.760
0.148
0.294
0.657
0.750
0.091
0.231
0.083
0.223
0.081
0,220
80.7%
60.3%
82.2%
62.6%
2.3%
1.1%
96
0.191
0.345
0.154
0.298
0.275
0.422
0.075
0,200
0.079
0.205
0,075
0.201
ET7m2
192
0.458
0.556
0.243
0.378
0.484
0.552
0.107
0.248
0.121
0.259
0.111
0.250
336
0.606
0.624
0.515
0.539
1.138
0.909
0.146
0.293
0.150
0.295
0.148
0.294
1.175
0.387
0.346
IMP.
33.4%
23.0%
82.8%
63.2%
8.5%
4.1%
18


Reviews:
[{"review_id": "9FV3KVLE8u", "reviewer": "Reviewer_8foj", "summary": "This paper addresses the problem of **distribution shifts in time-series forecasting**, focusing specifically on **concept drift**—a relatively under-explored issue compared to temporal shift. The authors propose:\n\n1. **SAM**: A mechanism to identify invariant patterns in exogenous features across lookback and horizon windows, enabling more stable conditional distribution modeling.\n2. **ShiftS**: A unified, model-agnostic framework that first mitigates temporal shift (via normalization) and then concept drift (via SAM), improving generalization across diverse forecasting models.\n\nExtensive experiments on six real-world datasets show that ShiftS consistently boosts forecasting accuracy across multiple base models and outperforms existing distribution-shift baselines.", "questions": "1. How does SAM perform when $\\mathbf{X}^H$ is not available during training or is highly noisy? Have you tested scenarios with missing or imperfect exogenous data?\n2. Could SAM be adapted for online settings where concept drift occurs continuously? The paper criticizes online methods but does not explore whether SAM can be extended in that direction.\n3. The mutual information analysis is insightful—have you considered using $ I(\\mathbf{X}^H; \\mathbf{Y}^H) $ as a criterion for applying SAM in practice?\n4. The framework currently uses RevIN for temporal shift mitigation. Have you experimented with more advanced methods (e.g., SAN) in the full ShiftS pipeline, and if so, how do they compare?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- **Originality**: SAM is a novel approach to handling concept drift without relying on environment labels or online retraining.\n- **Quality**: The method is well-designed, with careful attention to both theoretical motivation and practical implementation.\n- **Clarity**: The problem formulation and methodology are clearly explained, and the experiments are thorough and convincing.\n- **Significance**: The paper fills a clear gap in the literature and provides a practical tool for improving time-series forecasting under distribution shifts.", "weaknesses": "- **Theoretical Guarantees**: The method lacks theoretical analysis (e.g., error bounds or convergence guarantees), which is noted in the limitations but could strengthen the contribution.\n- **Dependence on Horizon Exogenous Data**: SAM relies on $\\mathbf{X}^H$ , which may not always be available or accurately predictable in practice. The paper addresses this via surrogate forecasting, but the impact of prediction error on final performance is not deeply analyzed.\n- **Limited Scope**: The method is evaluated only on univariate forecasting with exogenous features. Its applicability to multivariate or purely endogenous settings remains unclear.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "kgVtVOsZT5", "reviewer": "Reviewer_ytQx", "summary": "This paper categorizes the general concept drift in time series into types: concept drift and temporal shift (as defined more precisely in Definition 2.1 and Definition 2.2). To solve the concept drift problem, it proposes the soft attention mechanism (SAM) to find the invariant patterns in lookback and horizon windows. The core idea of this paper is illustrated well in Fig. 1. A method-agnostic framework called ShiftTS is proposed to deal with both temporal and concept drifts in a unified framework. Experiments demonstrate the good performance of the proposed method.", "questions": "1.\tThe analysis in Section 4.2 looks reasonable to me. The improvement of the proposed method depends on the data and the base algorithm simultaneously. Fig.3(a) plots the performance gain vs. the mutual information between X and Y. In fact, this plot studies the effectiveness of ShiftTS w.r.t. the so-called concept drift defined in Def 2.2 in this paper. A good example is the Exchange dataset, which shows low mutual information but high performance improvement. Thus, it suggests that the performance is mainly due to the mitigation of the so-called temporal concept drift. This is also consistent of Fig. 3(b), which shows that the most significant performance improvement is between ShiftTS\\TS and Base. Therefore, at least on the Exchange dataset, the proposal of learning form surrogate feature $X_{SUR}$ looks incremental.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.\tThe paper is well written and easy to follow. The idea proposed is simple. \n2.\tThe invariant patterns are learned through the surrogate feature $X_{SUR}$ and this is the core contribution of this paper. The basic idea is to concatenate the lookback and horizon windows, and model the conditional distributions for local patterns using the soft attention matrix M. \n3.\tExperiments demonstrate the good performance of the proposed method.", "weaknesses": "1.\tThe categorization of temporal shift and concept drift is very similar to different sources of concept outlined in Section 2.1 in [R1], but in the context of time series with some differences (the temporal shift is for Y, and the concept drift is the same as Source II in [R1] ). \n2.\tThe method mitigating temporal shift (or the marginal distribution shift of Y) looks quite standard in the literature. \n3.\tThe proposal of mitigating concept drift may be incremental for some datasets and base algorithms.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "dg5jhIfqsB", "reviewer": "Reviewer_YbKf", "summary": "This paper identifies two types of distribution shifts in time series forecasting: temporal shift (marginal distribution) and concept drift (conditional distribution). The authors propose a new method, SAM (soft attention masking), to mitigate concept drift by learning invariant patterns from both lookback and *horizon* exogenous features ($X^L$ and $X^H$). This mechanism learns a surrogate feature, $X^{SUR}$, which is predicted as an auxiliary task. The paper also presents ShifTS, a model agnostic framework that first uses normalization (like RevIN) to handle temporal shift, and then uses a backbone model to jointly predict the target $Y^H$ and the surrogate $\\hat{X}^{SUR}$. Experiments on six datasets show that ShifTS consistently improves the performance of various backbone models, including current state of the art ones.", "questions": "1.  Can you please clarify how the SAM mechanism (Equation 1) specifically enforces invariance? The high weight patterns are defined as invariant, but it is unclear how the optimization process encourages this property over just learning a stable predictive signal.\n2.  To justify the complexity of SAM, could you add a baseline that replaces the $X^{SUR}$ target with the raw $X^H$? This would involve a multi task loss $\\mathcal{L} = \\mathcal{L}_{TS} + \\lambda \\cdot MSE(X^H, \\hat{X}^H)$. This comparison is essential to prove that the SAM slicing and attention is superior to just predicting the raw future features.\n3.  What is the impact of applying ShifTS to \"near-stationary\" datasets like Traffic or Weather, which were excluded? Does the method degrade performance in the absence of significant shifts, or does it robustly \"do no harm\"?\n4.  The aggregation step ($Agg(\\cdot)$ in Algorithm 1 and Figure 2) appears to be a key component. Could you provide more detail on its architecture and how the final $\\hat{Y}^H$ is computed from the initial forecast and the $\\hat{X}^{SUR}$ prediction?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper clearly distinguishes between temporal shift and concept drift, tackling a significant and practical problem in time series forecasting.\n- The core idea of using *horizon* exogenous features ($X^H$) to define a stable surrogate target ($X^{SUR}$) is novel. This surrogate acts as an effective regularization target during training, forcing the model to learn future relevant patterns.\n- The ShifTS framework is practical and model agnostic. It cleanly integrates a known temporal shift solution (normalization) with the proposed concept drift solution (SAM).\n- The experiments are comprehensive. They show consistent performance improvements across six datasets and multiple strong backbone models, and also outperform other distribution shift baselines.", "weaknesses": "- The claim that SAM finds \"invariant patterns\" is not well supported by the mechanism. The method (Equation 1) is a learnable attention mask, not an explicit invariance optimization like in IRM. It seems to learn a *useful compression* of future features, but calling it \"invariant\" is a strong claim that needs better justification.\n- The paper introduces significant complexity with the SAM module and the aggregation MLP. However, the performance gains on SOTA models like iTransformer are sometimes small (e.g., <5% MAE gain on ETTh2/ETTm2). The marginal benefit versus the added complexity is questionable in these cases.\n- A critical and much simpler baseline is missing. The paper argues predicting raw $X^H$ is too hard, but $X^{SUR}$ is easier. This assertion must be tested by comparing ShifTS to a simpler multi task model that just predicts the raw $X^H$ as the auxiliary task.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)