stat.MLMar 20, 2026

Deep Time-Series Forecasting in 10 Years: A Survey

Authors: Hao Wang, Licheng Pan, Qingsong Wen, Jialin Yu, Zhichao Chen, Chunyuan Zheng, Xiaoxi Li, Zhixuan Chu, +7 more

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Autocorrelation is a common property of time-series, where each observation is dependent on its predecessors. In deep time-series forecasting, it raises two central challenges: (1) designing backbone architectures to model autocorrelation in history sequences, and (2) devising loss functions to model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper reviews deep time-series forecasting from an autocorrelation modeling perspective, offering two contributions beyond existing surveys. First, it introduces a taxonomy that jointly covers both backbone architectures and loss functions, whereas prior surveys provide limited coverage of the latter. Second, it analyzes the motivations and insights underlying the surveyed literature from a unified autocorrelation perspective, providing a holistic overview of the field's evolution. Additional resources and details are available at https://github.com/Master-PLC/Awesome-TSF-Papers.

Figures & tables

Fig. 1 : The ACF at different lags on time-series datasets.
Fig. 2 : The visualization of representative temporal patterns and their ACFs.
AuthorYearTaxonomyBackbone ArchitectureLoss Function
   Non-TransformersTransformersPlug-insLikeEstShapeAlignDistBalCondGene
Wen et al. [ 41 ]2023Backbone architecture-✓-----
Li et al. [ 63 ]2024Backbone architecture✓✓-----
Wang et al. [ 2 ]2024Backbone architecture✓✓✓----
Casolaro et al. [ 64 ]2023Backbone architecture✓✓----✓
Liang et al. [ 62 ]2024Backbone architecture✓✓----✓
TABLE I : Overview of recent surveys.
Fig. 4 : Overview of representative non-Transformer architectures. Circular nodes represent model inputs and outputs.
Fig. 5 : Overview of representative Transformer architectures. The circlular nodes represent model input and output. The colored blocks indicate the primary modifications to adapt Transformer to time-series forecasting.
ModelYearBackboneTokenizerTextsCross-modal Alignment StrategyFine-tuned LLM parameters
     QueryReproPretrainFinetuning
PromptCast [ 110 ]2023BERTDiscrete✓✓----
LLMTime [ 111 ]2023GPT3Discrete-✓----
Time-LLM [ 112 ]2024LLaMAPatching✓-✓---
Time-FFM [ 113 ]2024GPT2Patching✓-✓---
GPT4TS [ 114 ]2023GPT2Patching----✓LN, PE
TABLE II : Overview of LLM-based time-series backbone architectures with standard self-attention token-mixers.
Fig. 6 : A typical layout of the plug-in layers following [ 115 ] , where the colored blocks represent the backbone architecture.
Loss functionYearTypeAgnosticAutoDiffAnalyticalInfer. freeParam. free
MSE [ 146 ]2021-✓✓✓✓✓
AutoMSE [ 174 ]2021Likelihood estimation✓✓✓✓✓
FreDF [ 14 ]2025Likelihood estimation✓✓✓✓✓
Time-o1 [ 42 ]2025Likelihood estimation✓✓✓✓✓
LatentTSF [ 175 ]2026Likelihood estimation✓✓✓--
DBLoss [ 176 ]2025Likelihood estimation✓✓✓✓✓
TABLE III : Overview of loss functions harnessing label autocorrelation.
Fig. 7 : The computation of loss functions based on likelihood estimation, where the dark blocks contain learnable parameters.
Fig. 8 : The computation of loss functions based on shape alignment, where the dark blocks contain learnable parameters.
Fig. 9 : The computation of loss functions based on distribution balancing, where the dark blocks contain learnable parameters.
Fig. 10 : The computation of loss functions based on conditional generation, where the dark blocks contain learnable parameters.
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

LossQDFDistDFTime-o1FreDFDBLossDilateSoft-DTWDTWMSE
(2026)(2026)(2026)(2025)(2025)(2019)(2017)(2003)(-)
MetricsMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
ETTm1960.3120.3530.3160.3570.3210.3570.3260.3550.3170.3460.3370.3670.3320.3630.3320.3640.3260.361
1920.3590.3800.3580.3800.3600.3780.3630.3800.3650.3740.3640.3840.3700.3860.3700.3860.3650.382
3360.3910.4030.3920.4040.3890.4000.3920.4000.3950.3980.3970.4060.4060.4090.4090.4100.3960.404
7200.4500.4380.4480.4370.4470.4350.4540.4400.4540.4330.4570.4430.4780.4500.4760.4480.4590.444
Appendix
TABLE IV : Comparable results with different loss functions.

Explore similar work

CardsList

  1. Reviving Error Correction in Modern Deep Time-Series Forecasting

    May 20, 2026Minh Hoang Nguyen, Dai Do, Huu Hiep Nguyen +3Time Series ForecastingTime Series

    Deakin Applied AI Initiative, Deakin University, Australia.

  2. Time-o1: Time-Series Forecasting Needs Transformed Label Alignment

    May 23, 2025Hao Wang, Licheng Pan, Zhichao Chen +5

    Xiaohongshu Inc. · State Key Lab of General AI, School of Intelligence Science and Technology, Peking University · Gaoling School of Artificial Intelligence, Renmin University of China +4

  3. FreDF: Learning to Forecast in the Frequency Domain

    Feb 4, 2024Hao Wang, Licheng Pan, Zhichao Chen +6

    Department of Control Science and Engineering, Zhejiang University · School of Automation, Central South University · Trust and Safety Team, TikTok Sydney, ByteDance Inc. +3