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Advanced Methods for Time Series Forecasting

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: 30 December 2025 | Viewed by 12230

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Dr. Camelia Delcea

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Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, 010552 Bucharest, Romania
Interests: energy economics; economic cybernetics; consumer behavior; agent-based modeling; sustainable development; gray systems theory; neutrosophic theory
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Prof. Dr. Nora Monica Chirita

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Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, 010552 Bucharest, Romania
Interests: economic cybernetics; consumer behavior; systems analysis; systems diagnosis; dynamics; sustainable development; circular economy
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Special Issue Information

Dear Colleagues,

In today’s world, which is highly driven by data, time series forecasting has become an essential tool across numerous industries. The process of accurately predicting future trends based on historical data has become crucial for decision-making processes, risk management, and planning in general. As technology continues to advance, the methods for analyzing and forecasting time series data continue to follow these advancements steps by becoming more precise, adaptive, and scalable in the face of real-world challenges.

The present Special Issue on "Advanced Methods for Time Series Forecasting" aims to explore cutting-edge methodologies and approaches that are transforming the field of time series analysis. With the advancement of artificial intelligence and the rise of hybrid models, a variety of options for handling complex data have become available, which have the potential to capture intricate patterns, nonlinear relationships, and long-term dependencies that traditional methods might overlook.

We welcome submissions from both theoretical and applied perspectives, including empirical research, case studies, comparative analyses, and reviews.

We look forward to receiving your contributions.

Dr. Camelia Delcea
Prof. Dr. Nora Monica Chirita
Guest Editors

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Keywords

time series analysis
complex data
AI
hybrid models
data analysis

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Published Papers (9 papers)

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Research

24 pages, 2214 KB

Open AccessArticle

MMHFormer: Multi-Source and Multi-View Hierarchical Transformer for Traffic Flow Prediction

by Han Wu, Guoqing Teng, Hao Wu, Zicheng Qiu and Meng Zhao

Appl. Sci. 2025, 15(23), 12804; https://doi.org/10.3390/app152312804 - 3 Dec 2025

Viewed by 218

Abstract

Traffic flow prediction is a vital component of Intelligent Transportation Systems (ITSs), playing a key role in proactive traffic management and the optimization of urban mobility. However, the complex spatial–temporal dependencies, dynamic variations, and external factors in traffic networks present significant challenges for accurate predictions. In this paper, we propose MMHFormer, a novel multi-source, multi-view hierarchical Transformer model specifically designed for traffic flow prediction. MMHFormer incorporates three key innovations: (1) a multi-source gated embedding layer that integrates diverse multidimensional inputs, including spatial Laplacian embeddings, temporal periodic embeddings, and traffic occupancy embeddings, to better capture the complex dynamics of traffic conditions; (2) a hierarchical multi-view spatial attention module that models global, local, and dynamic similarity-based spatial dependencies, effectively addressing the spatial heterogeneity of traffic flows; (3) a hierarchical two-stage temporal attention mechanism that captures global temporal dependencies while adapting to node-specific temporal variations. Extensive experiments conducted on four benchmark traffic datasets demonstrate that MMHFormer outperforms state-of-the-art methods, achieving significant improvements in prediction accuracy. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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25 pages, 1326 KB

Open AccessArticle

KOSLM: A Kalman-Optimal Hybrid State-Space Memory Network for Long-Term Time Series Forecasting

by Xin Tan, Lei Wang, Mingwei Wang and Ying Zhang

Appl. Sci. 2025, 15(23), 12684; https://doi.org/10.3390/app152312684 - 29 Nov 2025

Viewed by 361

Abstract

Long-term time series forecasting (LTSF) remains challenging, as models must capture long-range dependencies and remain robust to noise accumulation. Traditional recurrent models, such as Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM), often suffer from instability and information degradation over extended horizons. The state-of-the-art method xLSTMTime improves memory retention through exponential gating and enhanced memory-transition rules, but it still lacks principled guidance. To address these issues, we propose the Kalman-Optimal Selective Long-Term Memory (KOSLM) model, which embeds a Kalman-optimal selective mechanism driven by the innovation signal within a structured state-space reformulation of LSTM. KOSLM dynamically regulates information propagation and forgetting to minimize state estimation uncertainty, providing both theoretical interpretability and practical efficiency. Extensive experiments across energy, finance, traffic, healthcare, and meteorology datasets show that KOSLM reduces mean squared error (MSE) by 14.3–38.9% compared with state-of-the-art methods, with larger gains at longer horizons. The model is lightweight, scalable, and achieves up to 2.5× speedup over Mamba-2. Beyond benchmarks, KOSLM is further validated on real-world Secondary Surveillance Radar (SSR) tracking under noisy and irregular sampling, demonstrating robust and generalizable long-term forecasting performance. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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22 pages, 2517 KB

Open AccessArticle

A Novel Hybrid Framework for Stock Price Prediction Integrating Adaptive Signal Decomposition and Multi-Scale Feature Extraction

by Junqi Su, Raymond Y. K. Lau, Yuefeng Du, Jia Yu and Hui Zhang

Appl. Sci. 2025, 15(23), 12450; https://doi.org/10.3390/app152312450 - 24 Nov 2025

Viewed by 678

Abstract

To address the issue of low prediction accuracy due to the inherent high noise and non-stationary characteristics of stock price series, this paper proposes a novel stock price prediction framework (CVASD-MDCM-Informer) that integrates adaptive signal decomposition with multi-scale feature extraction. The framework first employs a CVASD module, which is a variational mode decomposition (VMD) method adaptively optimized by a porcupine optimization (CPO) algorithm, to decompose the original stock price series into a series of intrinsic mode functions (IMFs) with different frequency characteristics, effectively separating noise and multi-frequency signals. Subsequently, the decomposed components are input into a prediction network based on Informer. In the feature extraction phase, this paper designs a multi-scale dilated convolution module (MDCM) to replace the standard convolution of the Informer, enhancing the model’s ability to capture short-term fluctuations and long-term trends by using convolution kernels with different dilation rates in parallel. Finally, the prediction results of each component are integrated to obtain the final predicted value. Experimental results on three representative industry datasets (Information Technology, Finance, and Consumer Staples) of the US S&P 500 index show that, compared to several advanced baseline models, the proposed framework demonstrates significant advantages in multiple evaluation metrics such as MAE, MSE, and RMSE. Ablation experiments further validate the effectiveness of the two core modules, CVASD and MDCM. The study indicates that the framework can effectively handle complex financial time series, providing a new solution for stock price prediction. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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13 pages, 3564 KB

Open AccessArticle

Iterative Forecasting of Short Time Series

by Evangelos Bakalis

Appl. Sci. 2025, 15(21), 11580; https://doi.org/10.3390/app152111580 - 29 Oct 2025

Viewed by 542

Abstract

We forecast short time series iteratively using a model based on stochastic differential equations. The recorded process is assumed to be consistent with an

α

-stable Lévy motion. The generalized moments method provides the values of the scaling exponent and the parameter

α

[...] Read more.

We forecast short time series iteratively using a model based on stochastic differential equations. The recorded process is assumed to be consistent with an

α

-stable Lévy motion. The generalized moments method provides the values of the scaling exponent and the parameter

α

, which determine the form of the stochastic term at each iteration. Seven weekly recorded economic time series—the DAX, CAC, FTSE100, MIB, AEX, IBEX, and STOXX600—were examined for the period from 2020 to 2025. The parameter

α

is always 2 for the four of them, FTSE100, AEX, IBEX, and STOXX600, indicating quasi-Gaussian processes. For FTSE100, IBEX, and STOXX600, the processes are anti-persistent (H < 0.5).The rest of the examined markets show characteristics of uncorrelated processes whose values are drawn from either a log-normal or a log-Lévy distribution. Further, all processes are multifractal, as the non-zero value of the mean intermittency indicates. The model’s forecasts, with the time horizon always one-step-ahead, are compared to the forecasts of a properly chosen ARIMA model combined with Monte Carlo simulations. The low values of the absolute percentage error indicate that both models function well. The model’s outcomes are further compared to ARIMA forecasts by using the Diebold–Mariano test, which yields a better forecast ability for the proposed model since it has less average loss. The ability and accuracy of the model to forecast even small time series is further supported by the low value of the absolute percentage error; the value of 4 serves as an upper limit for the majority of the forecasts. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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23 pages, 5146 KB

Open AccessArticle

Spatio-Temporal Multi-Graph Convolution Traffic Flow Prediction Model Based on Multi-Source Information Fusion and Attention Enhancement

by Wenjing Li, Zhongning Sun and Yao Wan

Appl. Sci. 2025, 15(20), 11295; https://doi.org/10.3390/app152011295 - 21 Oct 2025

Viewed by 735

Abstract

Traffic flow prediction plays a vital role in intelligent transportation systems, directly affecting travel scheduling, road planning, and traffic management efficiency. However, traditional methods often struggle to capture complex spatiotemporal dependencies and integrate heterogeneous data sources. To overcome these challenges, we propose a Spatio-temporal Multi-graph Convolution Traffic Flow Prediction Model based on Multi-source Information Fusion and Attention Enhancement (MIFA-ST-MGCN). The model adopts adaptive data fusion strategies according to spatiotemporal characteristics, achieving effective integration through feature concatenation and multi-graph structure construction. A spatiotemporal attention mechanism is designed to dynamically capture the varying contributions of different adjacency relations and temporal dependencies, thereby enhancing feature representation. In addition, recurrent units are combined with graph convolutional networks to model spatiotemporal data and generate more accurate prediction results. Experiments conducted on a real-world traffic dataset demonstrate that the proposed model achieves superior performance, reducing the mean absolute error by 3.57% compared with mainstream traffic flow prediction models. These results confirm the effectiveness of multi-source fusion and attention enhancement in improving prediction accuracy. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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20 pages, 1278 KB

Open AccessArticle

Hybrid ML/DL Approach to Optimize Mid-Term Electrical Load Forecasting for Smart Buildings

by Ayaz Hussain, Giuseppe Franchini, Muhammad Akram, Muhammad Ehtsham, Muhammad Hashim, Lorenzo Fenili, Silvio Messi and Paolo Giangrande

Appl. Sci. 2025, 15(18), 10066; https://doi.org/10.3390/app151810066 - 15 Sep 2025

Viewed by 1510

Abstract

Most electric energy consumption in the building sector is provided by fossil fuels, leading to high greenhouse gas emissions. However, the increasing need for sustainable infrastructure has triggered a significant trend toward smart buildings, which enable optimal and efficient resource usage. In this context, accurate mid-term energy load forecasting is crucial for energy management. This study proposes a hybrid forecasting model obtained through the combination of machine learning (ML) and deep learning (DL) approaches designed to enhance forecasting accuracy at an hourly granularity. The hybrid two-layer architecture first investigates the model’s performance individually, such as decision tree (DT), random forest (RF), support vector regression (SVR), Extreme Gradient Boosting (XGBoost), FireNet, and long short-term memory (LSTM), and then combines them to leverage their complementary strengths in a two-layer hybrid design. The performance of these models is assessed on smart building energy datasets with weather data, and their accuracy is measured through performance metrics such as mean squared error (MSE), root mean squared error (RMSE), and R-squared (

R^{2}

). The collected results show that the XGBoost outperformed other ML models. However, the hybrid model obtained by combining FireNet and XGBoost models delivers the highest overall accuracy for the performance parameters. These findings highlight the effectiveness of hybrid models in terms of prediction accuracy. This research contributes to reliable energy forecasting and supports environmentally sustainable practices. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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18 pages, 3124 KB

Open AccessArticle

TFHA: A Time–Frequency Harmonic Attention Framework for Analyzing Digital Management Strategy Impact Mechanisms

by Shu Cao and Can Zhou

Appl. Sci. 2025, 15(18), 9989; https://doi.org/10.3390/app15189989 - 12 Sep 2025

Viewed by 694

Abstract

In the era of digital transformation, understanding and quantifying the mechanisms by which management strategies influence organizational performance is a critical yet insufficiently addressed challenge. Existing analytical models often overlook the intertwined temporal dependencies, cross-frequency interactions, and heterogeneous contextual factors that shape strategic impacts in real-world settings. To address these limitations, we propose TFHA (Time–Frequency Harmonic Attention), a unified framework that integrates frequency-domain pattern decomposition, temporal context encoding, and multi-view representation learning to analyze and forecast strategy-driven performance outcomes in an interpretable manner. Specifically, a Fourier Frequency Attention module captures multi-scale periodic patterns underlying strategic behaviors, while a temporal feature embedding component encodes both static calendar effects and dynamic, event-triggered fluctuations. Furthermore, a Contrastive Time–Frequency Representation Enhancement module aligns semantic, behavioral, and quantitative perspectives to produce robust, context-aware representations. Experiments on four real-world datasets from digital tourism management platforms demonstrate that TFHA reduces MAE by up to 18.5% compared with strong baselines such as Autoformer, Informer, and ETSformer, while exhibiting strong robustness under input perturbations and cross-domain generalization. These results highlight TFHA’s potential as both a predictive tool and an analytical lens for revealing the time–frequency dynamics underpinning the effectiveness of digital brand management strategies in tourism contexts. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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38 pages, 5792 KB

Open AccessArticle

Bibliometric Insights into Time Series Forecasting and AI Research: Growth, Impact, and Future Directions

by Adrian Domenteanu, Paul Diaconu and Camelia Delcea

Appl. Sci. 2025, 15(11), 6221; https://doi.org/10.3390/app15116221 - 31 May 2025

Cited by 4 | Viewed by 3655

Abstract

Considering that nowadays the economy plays a crucial role, time series forecasting has become an essential tool across various economic areas and industries. The process of predicting future trends based on historical values in a reliable and accurate manner has generated numerous benefits, such as simplified decision-making processes or strategic planning and reduced risk management. Furthermore, with the advancement made through the use of Artificial Intelligence (AI) methods, time series forecasting has quickly become more precise, adaptive, and scalable, being able to better overcome real-world challenges. In this context, the present paper analyzes the implications of artificial intelligence in time series forecasting by evaluating the scientific articles from the field indexed in Clarivate Analytics’ Web of Science Core Collection database. Through a bibliometric approach, the research identifies key journals, affiliations, authors, and countries, as well as the collaboration networks among authors and countries. It also analyzes the most frequently used keywords and authors’ keywords. The annual growth rate of 23.11% indicates sustained interest among researchers. Prominent journals such as IEEE Access, Energies, Mathematics, Applied Sciences—Basel, and Applied Energy have been the home for the most published papers in this field. Further, thanks to the Biblioshiny library in R, a variety of visualizations have been created, including thematic maps, three-field plots, and word clouds. A comprehensive review of the most cited papers has been performed to highlight the role of AI in time series forecasting. Research results and methods confirmed the versatility of the topics, which have been applied in various fields, such as, but not limited to, finance, energy, climate, and healthcare, and are further discussed. Cutting-edge methodologies and approaches that lead to the transformation of the field of time series analysis in the context of AI are uncovered and discussed through the use of thematic maps. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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20 pages, 9086 KB

Open AccessArticle

Monte Carlo Dropout Neural Networks for Forecasting Sinusoidal Time Series: Performance Evaluation and Uncertainty Quantification

by Unyamanee Kummaraka and Patchanok Srisuradetchai

Appl. Sci. 2025, 15(8), 4363; https://doi.org/10.3390/app15084363 - 15 Apr 2025

Cited by 6 | Viewed by 2517

Abstract

Accurately forecasting sinusoidal time series is essential in various scientific and engineering applications. However, traditional models such as the seasonal autoregressive integrated moving average (SARIMA) rely on assumptions of linearity and stationarity, which may not adequately capture the complex periodic behaviors of sinusoidal data, including varying amplitudes, phase shifts, and nonlinear trends. This study investigates Monte Carlo dropout neural networks (MCDO NNs) as an alternative approach for both forecasting and uncertainty quantification. The performance of MCDO NNs is evaluated across six sinusoidal time series models, each exhibiting different dynamic characteristics. Results indicate that MCDO NNs consistently outperform SARIMA in terms of root mean square error, mean absolute percentage error, and the coefficient of determination, while also producing more reliable prediction intervals. To assess real-world applicability, the airline passenger dataset is used, demonstrating MCDO’s ability to effectively capture periodic structures. These findings suggest that MCDO NNs provide a robust alternative to SARIMA for sinusoidal time series forecasting, offering both improved accuracy and well-calibrated uncertainty estimates. Full article

(This article belongs to the Special Issue Advanced Methods for Time Series Forecasting)

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