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Recently, frequency transformation (FT) has been increasingly incorporated into deep learning models to significantly enhance state-of-the-art accuracy and efficiency in time series analysis. The advantages of FT, such as high efficiency…

Machine Learning · Computer Science 2025-06-16 Kun Yi , Qi Zhang , Wei Fan , Longbing Cao , Shoujin Wang , Guodong Long , Liang Hu , Hui He , Qingsong Wen , Hui Xiong

The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-02-04 Sudhanshu Kulkarni , Burlen Loring , E. Wes Bethel

Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…

Machine Learning · Computer Science 2020-11-25 Tsung-Yu Hsieh , Suhang Wang , Yiwei Sun , Vasant Honavar

Current approaches for time series forecasting, whether in the time or frequency domain, predominantly use deep learning models based on linear layers or transformers. They often encode time series data in a black-box manner and rely on…

Machine Learning · Computer Science 2025-10-14 Cheng He , Xijie Liang , Zengrong Zheng , Patrick P. C. Lee , Xu Huang , Zhaoyi Li , Hong Xie , Defu Lian , Enhong Chen

This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…

Chaotic Dynamics · Physics 2007-05-23 Carlos R. Fadragas , Juan V. Lorenzo-Ginori , Ruben Orozco-Morales

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…

Machine Learning · Computer Science 2023-11-30 Jingyi Hou , Zhen Dong , Jiayu Zhou , Zhijie Liu

Multivariate Time Series Forecasting (MTSF) plays a crucial role across diverse fields, ranging from economic, energy, to traffic. In recent years, deep learning has demonstrated outstanding performance in MTSF tasks. In MTSF, modeling the…

Machine Learning · Computer Science 2026-01-28 Xiangfei Qiu , Hanyin Cheng , Xingjian Wu , Junkai Lu , Jilin Hu , Chenjuan Guo , Christian S. Jensen , Bin Yang

A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an…

Numerical Analysis · Mathematics 2024-02-28 Michael Sorochan Armstrong , José Carlos Pérez-Girón , José Camacho , Regino Zamora

Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…

Signal Processing · Electrical Eng. & Systems 2021-09-10 Fang-Jia Yan , Bing-Zhao Li

Events such as the Financial Crisis of 2007-2008 or the COVID-19 pandemic caused significant losses to banks and insurance entities. They also demonstrated the importance of using accurate equity risk models and having a risk management…

Computational Finance · Quantitative Finance 2021-09-28 Eduardo Ramos-Pérez , Pablo J. Alonso-González , José Javier Núñez-Velázquez

The key problem in multivariate time series (MTS) analysis and forecasting aims to disclose the underlying couplings between variables that drive the co-movements. Considerable recent successful MTS methods are built with graph neural…

Machine Learning · Computer Science 2022-10-11 Kun Yi , Qi Zhang , Liang Hu , Hui He , Ning An , LongBing Cao , ZhenDong Niu

Multivariate time-series (MTS) forecasting is a paramount and fundamental problem in many real-world applications. The core issue in MTS forecasting is how to effectively model complex spatial-temporal patterns. In this paper, we develop a…

Machine Learning · Computer Science 2024-02-16 Jinliang Deng , Xiusi Chen , Renhe Jiang , Du Yin , Yi Yang , Xuan Song , Ivor W. Tsang

The field of eXplainable Artificial Intelligence (XAI) has greatly advanced in recent years, but progress has mainly been made in computer vision and natural language processing. For time series, where the input is often not interpretable,…

Machine Learning · Computer Science 2023-03-14 Johanna Vielhaben , Sebastian Lapuschkin , Grégoire Montavon , Wojciech Samek

Financial time-series forecasting has long been a challenging problem because of the inherently noisy and stochastic nature of the market. In the High-Frequency Trading (HFT), forecasting for trading purposes is even a more challenging task…

Computational Engineering, Finance, and Science · Computer Science 2019-06-11 Dat Thanh Tran , Alexandros Iosifidis , Juho Kanniainen , Moncef Gabbouj

High-dimensional functional time series offers a powerful framework for extending functional time series analysis to settings with multiple simultaneous dimensions, capturing both temporal dynamics and cross-sectional dependencies. We…

Methodology · Statistics 2025-12-08 Haixu Wang , Tianyu Guan , Han Lin Shang

Neural collaborative filtering (NCF) and recurrent recommender systems (RRN) have been successful in modeling user-item relational data. However, they are also limited in their assumption of static or sequential modeling of relational data…

Machine Learning · Computer Science 2018-02-14 Xian Wu , Baoxu Shi , Yuxiao Dong , Chao Huang , Nitesh Chawla

Time Series Forecasting (TSF) is used to predict the target variables at a future time point based on the learning from previous time points. To keep the problem tractable, learning methods use data from a fixed length window in the past as…

Machine Learning · Computer Science 2022-04-26 Jimeng Shi , Mahek Jain , Giri Narasimhan

Multivariate time-series forecasting holds immense value across diverse applications, requiring methods to effectively capture complex temporal and inter-variable dynamics. A key challenge lies in uncovering the intrinsic patterns that…

Machine Learning · Computer Science 2025-03-12 Liang Yu , Lai Tu , Xiang Bai

Long-term Time Series Forecasting (LTSF) is critical for numerous real-world applications, such as electricity consumption planning, financial forecasting, and disease propagation analysis. LTSF requires capturing long-range dependencies…

Machine Learning · Computer Science 2024-10-04 Aitian Ma , Dongsheng Luo , Mo Sha

While Transformers excel in language and vision-where inputs are semantically rich and exhibit univariate dependency structures-their architectural complexity leads to diminishing returns in time series forecasting. Time series data is…

Machine Learning · Computer Science 2025-06-09 Yash Vijay , Harini Subramanyan