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DBLoss: Decomposition-based Loss Function for Time Series Forecasting

Xiangfei Qiu, Xingjian Wu, Hanyin Cheng, Xvyuan Liu, Chenjuan Guo, Jilin Hu, Bin Yang

arXiv:2510.23672v1cs.LG

TL;DR

MSE may not capture seasonality or trend in the forecasting horizon, even when the model decomposes contextual data. DBLoss uses EMA to decompose forecasts and targets into seasonal and trend components, computes separate weighted losses, and is reported to surpass state-of-the-art performance on eight real-world datasets.

  • Problem

    MSE can fail to capture seasonality or trend within the forecasting horizon, even when forward-pass decomposition models those structures separately.

    Source: §1 · p. 2

  • Method

    DBLoss uses exponential moving averages to decompose forecasts and targets into seasonal and trend components, then computes and weights their losses separately.

    Source: §1 · p. 2, §3.2 · p. 4, §3.3 · p. 5

  • Results

    DBLoss is reported to surpass state-of-the-art performance on eight real-world datasets.

    Source: §5 · p. 9

  • Takeaways & Limitations

    DBLoss is presented as a general loss applicable to arbitrary deep neural networks with negligible cost.

    Source: §1 · p. 2

Abstract

from arXiv · show

Time series forecasting holds significant value in various domains such as economics, traffic, energy, and AIOps, as accurate predictions facilitate informed decision-making. However, the existing Mean Squared Error (MSE) loss function sometimes fails to accurately capture the seasonality or trend within the forecasting horizon, even when decomposition modules are used in the forward propagation to model the trend and seasonality separately. To address these challenges, we propose a simple yet effective Decomposition-Based Loss function called DBLoss. This method uses exponential moving averages to decompose the time series into seasonal and trend components within the forecasting horizon, and then calculates the loss for each of these components separately, followed by weighting them. As a general loss function, DBLoss can be combined with any deep learning forecasting model. Extensive experiments demonstrate that DBLoss significantly improves the performance of state-of-the-art models across diverse real-world datasets and provides a new perspective on the design of time series loss functions.

1 Introduction

Forecasting models seek to capture seasonality and trend, but distance-based losses may fail to model those structures in the forecast horizon, even when decomposition is used on contextual data. DBLoss decomposes the forecast and target into seasonal and trend components, computes separate losses, and combines them with weighting; it is presented as broadly applicable and effective across real-world datasets.

1 Introduction

  • Forecasting models are designed to capture seasonality and trend because the paper identifies these as inherent patterns relevant to accurate predictions.The introduction names economics, traffic, energy, and AIOps as application domains.Source: §1 · p. 1
  • Even with decomposition in the forward pass, distance-based losses such as MSE may poorly capture seasonality, trend, or both within the forecasting horizon.The paper argues that contextual decomposition does not ensure that these structures are modeled effectively in the predictions.Source: §1 · p. 2
  • DBLoss uses exponential moving averages to decompose the forecast and target into seasonal and trend components, then separately computes and weights their losses.The method is presented as a general loss that can be combined with deep-learning forecasting models.Source: §1 · p. 2
  • DBLoss is reported to generally surpass state-of-the-art performance on eight real-world datasets and to apply to arbitrary deep neural networks with negligible cost.The paper also reports quantitative analyses and qualitative visualizations to evaluate its effectiveness.Source: §1 · p. 2

2 Related works

The related work reviews forecasting methods that model temporal structure and methods that adapt the loss to series structure. It positions DBLoss as a loss-function approach that decomposes the forecast horizon into trend and seasonal components.

2.1 Time Series Forecasting Methods

  • Forecasting approaches span statistical, machine-learning, deep-learning, and foundation methods, with deep models using varied architectures and foundation models targeting transfer across domains.The cited examples include neural sequence, Transformer, and MLP-based methods; foundation approaches include LLM-based and time-series pre-trained models.Source: §2.1 · pp. 2–3

2.2 Loss Functions for Time Series Forecasting

  • Forecasting losses include shape-based, dependency-based, and patch-based structural approaches; DBLoss instead decomposes the forecasting horizon to represent trend and seasonality.The review notes that high computational complexity restricts some DTW-based shape losses in large-scale settings.Source: §2.2 · p. 3

3 DBLoss

DBLoss predicts future time points with an arbitrary backbone, then decomposes prediction and target into seasonal and trend components using EMA. It computes component losses separately and combines them with a weighted loss that adaptively aligns their scales.

3 DBLoss

  • Time series forecasting predicts the next F timestamps from historical observations, with channels indexing the dimensions of the series.The paper denotes the series as X and the future observations as Y.Source: §3 · pp. 3–4

3.1 Overview

  • The pipeline generates a prediction with an arbitrary backbone, decomposes prediction and ground truth into seasonal and trend components, and combines their component errors into the final loss.The component errors are combined using a weighted sum.Source: §3.1 · p. 4

3.2 EMA Decomposition Module

  • DBLoss uses EMA decomposition on both prediction and ground truth, treating the residual as seasonality and the smoothed component as trend.The decomposition module takes a time series and smoothing factor α as input and returns seasonal and trend components.Source: §3.2 · p. 4

3.3 Weighted Loss Function

  • The total loss weights separate seasonal and trend losses, while adaptively adjusting trend loss by their relative magnitudes and detaching gradients through the alignment ratio.β balances the seasonal and trend contributions; ε is used for numerical stability.Source: §3.3 · p. 5

4 Experiments

The experiments evaluate DBLoss across forecasting models, datasets, and settings, with results generally favoring DBLoss over MSE. Additional analyses examine zero-shot and few-shot transfer, training dynamics, hyperparameters, and forecast visualizations.

4.1 Setup

  • Experiments use eight benchmarks and eight SOTA backbones, reporting MSE and MAE at horizons 96, 192, 336, and 720.Baseline results are taken from TFB, with the loss function replaced and no other script modifications.Source: §4.1 · p. 5

4.2 Main results

  • DBLoss improves performance across all backbone models and significantly outperforms MSE loss in most cases.Table 1 reports MSE and MAE for long-term multivariate forecasting across four horizons.Source: §4.2 · pp. 5–6, Table 1 · p. 6

4.3 Comparison with Other Loss Functions

  • DBLoss achieves the lowest MSE and MAE in most cases against other loss functions across datasets and forecasting horizons.The comparison uses DLinear on ETTh2, ETTm1, and Traffic.Source: §4.3 · p. 6, Table 2 · p. 7

4.4 Zero-shot Forecasting Results

  • In zero-shot forecasting at horizon 720, DBLoss outperforms MSE in most cases across target datasets and sampling frequencies.ETTh1, ETTh2, ETTm1, and ETTm2 are used sequentially as source datasets, with remaining datasets as targets.Source: Table 3 · p. 7, §4.4 · p. 7

4.5 Results on Time Series Foundation Models

  • In 5% few-shot experiments, adding DBLoss during fine-tuning consistently outperforms standard MSE on four time-series foundation models.Table 4 reports average MSE and MAE across four forecasting lengths.Source: §4.5 · p. 7, Table 4 · p. 8

4.6 Impact of DBLoss on Generalization

  • Across four datasets, DBLoss yields higher training errors but lower testing errors than MSE.The authors also report greater test-loss stability with DBLoss on some datasets.Source: Figure 3 · p. 8, §4.6 · p. 8

4.7 Hyperparameter Sensitivity

  • A larger β raises the seasonal component’s loss weight, while a smaller α smooths the trend more and makes the seasonal component more prominent.The sensitivity figure covers DLinear on ETTh2 and Traffic at horizon 96.Source: §4.7 · p. 9, Figure 4 · p. 9

4.8 Forecasting Visualization

  • For ETTh1 samples, forecasts with DBLoss are closer to the ground truth than forecasts with MSE.The paper attributes this to DBLoss encouraging learning of seasonal and trend patterns.Source: §4.8 · p. 9, Figure 5 · p. 9

5 Conclusion

The conclusion presents DBLoss as a response to MSE’s occasional failure to capture forecast-horizon seasonality or trend. It decomposes predictions and targets with exponential moving averages, weights separate component losses, and reports state-of-the-art performance across eight real-world datasets.

5 Conclusion

  • DBLoss surpasses state-of-the-art performance across eight real-world datasets when introduced into baseline models.The authors also state that the method is generally applicable to deep learning forecasting models with negligible cost.Source: §5 · p. 9
  • DBLoss uses exponential moving averages to decompose predictions and targets into forecast-horizon seasonal and trend components, then weights their separate losses.Source: §5 · p. 9
  • The method addresses cases where MSE fails to capture forecast-horizon seasonality or trend, even when forward-propagation decomposition modules are used.Source: §5 · p. 9

NeurIPS Paper Checklist

The authors answer yes when asked whether the abstract and introduction accurately reflect the paper’s contributions and scope. The checklist says those claims should match the results and communicate important assumptions and limitations.

NeurIPS Paper Checklist

  • The authors answer yes and state that the abstract and introduction accurately reflect the paper’s contributions.Source: NeurIPS Paper Checklist · p. 15
  • The checklist says claims should match theoretical and experimental results and reflect how well they may generalize to other settings.Source: NeurIPS Paper Checklist · p. 15
  • The checklist says the abstract and introduction should state the claims, contributions, assumptions, and limitations.Source: NeurIPS Paper Checklist · p. 15

2. Limitations

The checklist response points readers to Appendix H for the paper’s discussion of DBLoss limitations. It also reports standard deviations in Appendix E and states that experimental details, code, and datasets are available for reproduction.

2. Limitations

  • The authors state that DBLoss limitations are discussed in Appendix H, but these passages do not specify the limitations themselves.Source: §2 · p. 15
  • The authors say complete experimental details are in Section 4.1 and full reproducible code and datasets are shared in an anonymous repository.Source: §2 · p. 16
  • The authors report standard deviations for all loss functions under different settings in Appendix E.Source: §2 · p. 17
  • The authors describe DBLoss as generally applicable to arbitrary deep neural networks with negligible cost.Source: §2 · p. 18

A Datasets

The datasets subsection describes eight forecasting benchmarks and points to a table of dataset statistics. The related-works subsection outlines forecasting-method categories, their development, and foundation methods aimed at cross-domain generalization.

A Datasets

  • The evaluation uses eight forecasting benchmarks: four ETT subsets, Weather, Electricity, Solar, and Traffic; Table 5 is identified as reporting dataset statistics.The ETT subsets span hourly and 15-minute data, while the other datasets cover weather, electricity consumption, solar production, and traffic occupancy.Source: A Datasets · p. 22, Table 5 · p. 22

B Related Works

  • Time-series forecasting methods are grouped into statistical learning, machine learning, deep learning, and foundation approaches.Source: B Related Works · p. 22
  • Foundation methods include LLM-based and time-series-pretrained approaches, with the latter pretraining on multidomain data to learn transferable, domain-agnostic features.Source: B Related Works · p. 22

C Theoretical Proofs

The theoretical analysis assumes that trend and seasonal components are highly independent. It represents both the observed series and the model prediction as sums of trend and seasonal components.

C Theoretical Proofs

C.1 Problem Formulation

  • The formulation expresses the observed series and model prediction as sums of trend and seasonal components.Source: §C.1 · p. 23

C.2 Analysis of MSE Loss

The analysis attributes interference between trend and seasonal optimization under MSE to a coupled term, while DBLoss separates their losses. The supplied efficiency results report a small training-time increase for PatchTST that becomes less pronounced as dataset size grows.

C.2 Analysis of MSE Loss

  • MSE's expansion includes a cross term between trend and seasonal errors that can disproportionately affect total loss.The analysis assumes the components are highly independent and gives the example of a poorly predicted trend paired with a well-captured seasonal component.Source: §C.2 · p. 23

C.3 Gradient Analysis of MSE

C.4 Analysis of DBLoss

  • DBLoss removes the gradient coupling term by optimizing trend and seasonal components separately.Its coefficients or distance norms can control each component's loss scale.Source: §C.4 · p. 24

D Visualization

  • Figure 6 compares forecasting visualizations using DBLoss and MSE as objective functions.Source: Figure 6 · p. 24

E Comparison with Other Loss Functions

F Efficiency

  • For PatchTST, DBLoss increases epoch-level training time over MSE, but the difference becomes more negligible as dataset size grows.The table reports average times across four forecasting horizons for each dataset.Source: Table 9 · p. 26, F Efficiency · p. 26

G Full Results on Time Series Foundation Models

The section presents foundation-model results under a 5% few-shot setting, reporting MSE and MAE across four forecasting horizons.

G Full Results on Time Series Foundation Models

  • The results cover MSE and MAE at forecasting lengths F ∈ {96, 192, 336, 720} under a 5% few-shot setting.Baseline parameters match those used in TSFM-Bench.Source: G Full Results on Time Series… · p. 26

H Limitations

The stated limitation is the lack of an automated strategy for selecting DBLoss's weighting and EMA smoothing parameters.

H Limitations

  • DBLoss lacks automated tuning for β and α, and this absence may limit performance improvement and generalization.A larger β weights the seasonal component more; a smaller α produces stronger smoothing and a more prominent seasonal component.Source: H Limitations · p. 26
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