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Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the…

Probability · Mathematics 2007-05-23 David R. Bickel

In the burgeoning ecosystem of Internet of Things, multivariate time series (MTS) data has become ubiquitous, highlighting the fundamental role of time series forecasting across numerous applications. The crucial challenge of long-term MTS…

Machine Learning · Computer Science 2024-11-06 Zhenwei Zhang , Linghang Meng , Yuantao Gu

The self-attention mechanism in Transformer architecture, invariant to sequence order, necessitates positional embeddings to encode temporal order in time series prediction. We argue that this reliance on positional embeddings restricts the…

Machine Learning · Computer Science 2024-08-21 Yongbo Yu , Weizhong Yu , Feiping Nie , Xuelong Li

Multivariate time series classification (MTSC) has attracted significant research attention due to its diverse real-world applications. Recently, exploiting transformers for MTSC has achieved state-of-the-art performance. However, existing…

Machine Learning · Computer Science 2024-05-24 Xuan-May Le , Ling Luo , Uwe Aickelin , Minh-Tuan Tran

In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to…

Rings and Algebras · Mathematics 2020-10-20 Joscha Diehl , Kurusch Ebrahimi-Fard , Nikolas Tapia

The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…

Data Analysis, Statistics and Probability · Physics 2021-05-28 Damian G. Kelty-Stephen , Elizabeth Lane , Madhur Mangalam

Time series are ubiquitous in many applications that involve forecasting, classification and causal inference tasks, such as healthcare, finance, audio signal processing and climate sciences. Still, large, high-quality time series datasets…

Machine Learning · Computer Science 2025-11-25 Yu-Hsiang Wang , Olgica Milenkovic

The massive generation of time-series data by largescale Internet of Things (IoT) devices necessitates the exploration of more effective models for multivariate time-series forecasting. In previous models, there was a predominant use of the…

Machine Learning · Computer Science 2024-03-15 Wenyong Han , Tao Zhu Member , Liming Chen , Huansheng Ning , Yang Luo , Yaping Wan

We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…

Machine Learning · Statistics 2019-12-06 David Tolpin

Time-series data originate from various applications that describe specific observations or quantities of interest over time. Their analysis often involves the comparison across different time-series data sequences, which in turn requires…

Machine Learning · Computer Science 2024-02-15 Kishansingh Rajput , Duong Binh Nguyen , Guoning Chen

We consider the problem of estimating a signal from its warped observations. Such estimation is commonly performed by altering the observations through some inverse-warping, or solving a computationally demanding optimization formulation.…

Signal Processing · Electrical Eng. & Systems 2021-12-03 İlker Bayram

Counterfactual explanations are increasingly proposed as interpretable mechanisms to achieve algorithmic recourse. However, current counterfactual techniques for time series classification are predominantly designed with static data…

Machine Learning · Computer Science 2025-12-17 Emmanuel C. Chukwu , Rianne M. Schouten , Monique Tabak , Mykola Pechenizkiy

Classification of time series is a growing problem in different disciplines due to the progressive digitalization of the world. Currently, the state-of-the-art in time series classification is dominated by The Hierarchical Vote Collective…

Machine Learning · Computer Science 2021-10-18 Francisco J. Baldán , José M. Benítez

Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…

Data Analysis, Statistics and Probability · Physics 2009-11-10 M. Ignaccolo , P. Allegrini , P. Grigolini , P. Hamilton , B. J. West

Time series analysis remains a major challenge due to its sparse characteristics, high dimensionality, and inconsistent data quality. Recent advancements in transformer-based techniques have enhanced capabilities in forecasting and…

Machine Learning · Computer Science 2024-05-29 Robert Leppich , Vanessa Borst , Veronika Lesch , Samuel Kounev

Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with…

Machine Learning · Computer Science 2026-01-29 Wei Li

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time…

Instrumentation and Methods for Astrophysics · Physics 2015-06-05 Jeffrey D. Scargle , Jay P. Norris , Brad Jackson , James Chiang

Sparse and irregularly sampled multivariate time series are common in clinical, climate, financial and many other domains. Most recent approaches focus on classification, regression or forecasting tasks on such data. In forecasting, it is…

Machine Learning · Computer Science 2020-04-08 Shivam Srivastava , Prithviraj Sen , Berthold Reinwald

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge…

Machine Learning · Computer Science 2026-05-20 Zinuo You , Jin Zheng , John Cartlidge

Time series are all around in real-world applications. However, unexpected accidents for example broken sensors or missing of the signals will cause missing values in time series, making the data hard to be utilized. It then does harm to…

Machine Learning · Computer Science 2020-11-24 Chenguang Fang , Chen Wang
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