time series analysis

Large language models (LLMs) inherently struggle to capture continuous temporal dynamics and explicit inter-variable dependencies in time series analysis. Method: This paper systematically reviews the emerging “time-series-to-image + vision model” paradigm, proposing the first dual-dimensional taxonomy: (i) time-series image encoding strategies (e.g., Gramian Angular Field, Markov Transition Field) and (ii) vision-model adaptation architectures (e.g., Vision Transformers, multimodal alignment, feature-decoupled reconstruction). It rigorously defines key pre-/post-processing challenges, surveys over 100 works, and establishes a unified evaluation framework. Contribution/Results: Empirical results demonstrate that vision-based approaches consistently outperform pure sequence models—achieving average accuracy gains of 5–12% across anomaly detection, forecasting, and classification tasks—thereby offering a promising new direction for time-series modeling.

This study addresses the challenge of degraded data quality—specifically outliers and missing values—in long-horizon time series forecasting, which critically undermines model robustness. We establish a unified evaluation framework to systematically benchmark mainstream models—including LSTM, Prophet, XGBoost, and Random Forest—under three realistic data conditions: complete, noisy (outlier-contaminated), and incomplete (missing-value) sequences, with ARIMA as the baseline. Methodologically, we employ sliding-window modeling, multi-step rolling prediction, and adaptive imputation for preprocessing. Our key contributions include: (i) a novel, interpretable algorithm selection guideline grounded in data characteristics and forecasting requirements; and (ii) empirical findings demonstrating that XGBoost reduces average MAE by 23% under noise, while Prophet exhibits superior stability for long-term trend forecasting. The results provide reproducible, principled guidance for industrial-scale time series modeling.

This study addresses the challenges of modeling and analyzing complex time series arising in astrophysics, meteorology, finance, and other domains by systematically integrating classical statistical methods—such as ARIMA, exponential smoothing, and state-space models—with modern machine learning techniques, including tree-based ensembles, hidden Markov models, Gaussian processes, and deep learning architectures like RNNs, CNNs, and Transformers. By distilling cross-disciplinary modeling principles, the work establishes a unified framework that combines theoretical rigor with practical guidance, offering researchers a comprehensive and extensible toolkit for time series analysis. This approach significantly enhances the capacity to handle temporal data across diverse scientific and applied contexts.

This work addresses the challenge that existing Mamba architectures struggle to effectively model the heterogeneous relationships between trend and seasonal components in non-stationary time series. To this end, it pioneers the integration of seasonal-trend decomposition with the Mamba framework, devising distinct modeling strategies tailored to the intrinsic characteristics of each component: a highly expressive variable-direction Mamba encoder captures the dynamic, high-dimensional interactions of seasonal patterns, while a lightweight MLP models the low-dimensional, long-term equilibrium relationships inherent in the trend component. Evaluated across multiple benchmark datasets, the proposed method significantly outperforms current Mamba variants and state-of-the-art decomposition-based models, achieving new state-of-the-art performance and demonstrating a precise alignment between model architecture and the statistical properties of time series data.

To address the challenge of effectively modeling multi-scale, nonlinear, and highly noisy temporal patterns in traffic flow data—features poorly captured by single-model approaches—this paper proposes a hybrid forecasting framework based on Seasonal and Trend decomposition using Loess (STL). The original time series is decomposed into trend, seasonal, and residual components, each modeled by a specialized algorithm: LSTM for long-term dependencies, ARIMA for periodic patterns, and XGBoost for nonlinear residuals. Final predictions are obtained via multiplicative ensemble integration. Compared to conventional single-model baselines, the proposed framework achieves superior prediction accuracy, enhanced interpretability, and improved robustness. Experiments on New York City traffic flow data demonstrate reductions in MAE and RMSE exceeding 15%, alongside an R² improvement of approximately 0.08, validating the efficacy of multi-component decomposition coupled with heterogeneous model collaboration.

Transformer-based models for time-series forecasting suffer from high computational complexity and overfitting, while standard MLPs struggle to capture complex, multi-scale temporal patterns. Method: This paper proposes an MLP-based adaptive multi-scale decomposition framework. Its core innovation is the Multi-scale Decomposable Mixture (MDM) module—integrated with Dual-Dependency Interaction (DDI) and Adaptive Multi-Predictor Synthesis (AMS)—enabling, for the first time, scale-aware joint time-frequency modeling within a pure MLP architecture. By explicitly decomposing and jointly modeling multi-scale dynamics and their cross-scale dependencies, the method significantly enhances pattern representation capability. Contribution/Results: Evaluated on multiple benchmark datasets, the approach achieves state-of-the-art accuracy and efficiency, outperforming leading Transformer- and MLP-based models with substantially lower computational overhead.

This work addresses the challenge of modeling highly coupled trend, multi-scale seasonal, and irregular residual components in multivariate time series forecasting, where cross-variable shared structures are difficult to capture effectively. To this end, the authors propose DecompSSM, a novel framework that employs three parallel deep state space model branches to explicitly learn trend, seasonality, and residual components. The approach integrates a learnable decomposition mechanism, an input-dependent adaptive temporal scale predictor, a cross-variable context refinement module, and an orthogonality-constrained auxiliary loss to enable end-to-end structure-aware disentangled modeling. Extensive experiments demonstrate that DecompSSM significantly outperforms strong baselines on benchmark datasets including ECL, Weather, ETTm2, and PEMS04, validating the effectiveness of component-wise state space modeling combined with global context refinement.

This paper addresses time-series analysis under exponential-family distributions by proposing a unified, analytically tractable framework for filtering, prediction, and smoothing. The core method constructs a convex combination estimator of the exponentially weighted log-likelihood and the expected log-likelihood, yielding—*for the first time under standard exponential families*—exact, linear, recursive closed-form filters, predictors, and smoothers. By integrating exponential-family statistical modeling with recursive Bayesian inference, the approach achieves both computational efficiency (O(1) per-step update) and statistical consistency (asymptotic optimality). Theoretical analysis provides rigorous guarantees on consistency and convergence. Empirical evaluation on synthetic and real-world datasets demonstrates superior efficiency and robustness compared to existing approximate or non-recursive methods.

This work proposes a neural-network-free feature-augmented forecasting approach for time series generated by Itô-type stochastic differential equations. The core idea lies in statistically reconstructing the unknown drift and diffusion coefficients directly from observed data: uniform reconstruction is employed alongside a non-uniform variant—equivalent to a stochastic Taylor expansion—to capture the state-dependent structure of these coefficients. A Gaussian mixture model is further integrated to achieve statistical separation of the reconstructed components. The resulting reconstruction parameters are incorporated as additional features into an autoregressive model, substantially enhancing predictive accuracy. Empirical results validate both the informational richness of these statistically derived features and the practical utility of the proposed methodology.

This work addresses the inconsistency among multi-granularity forecasts in online hierarchical time series prediction by proposing a reconciliation method that explicitly models hierarchical relationships through a graph structure. The approach characterizes forecast residuals using a matrix normal distribution and formulates a multivariate linear regression framework, integrating ridge regression, Bayesian estimation, and shrinkage principles. An efficient online recursive inference mechanism is developed to enable adaptive forecast reconciliation and uncertainty quantification. The method is validated on a district heating load forecasting task, demonstrating its effectiveness. To support practical deployment, the authors release PyOnlineForecast, an open-source toolkit for online hierarchical forecasting.

This work addresses the challenge of rapid dynamic shifts in streaming time series caused by abrupt environmental changes or varying input delays. The authors propose a system tensor representation based on Markov parameter sequences, modeling the streaming data as a dynamic mixture of delay systems. By constructing fixed-length tensor summaries that jointly encode system dynamics and input–output delay characteristics, the method enables efficient compression and retrieval of historical patterns through tensor decomposition. Within an online learning framework, the system dynamically selects the optimal submodel to match the current state, achieving strong adaptability to nonstationary time series while maintaining low memory overhead. Experimental results on real-world datasets demonstrate that the proposed approach significantly outperforms existing methods in both prediction accuracy and adaptation speed, particularly under highly nonstationary conditions.