New Challenges in Time Series and Statistics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 20 May 2025 | Viewed by 861

Special Issue Editor


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Guest Editor
Department of Mathematics, University of California, San Diego, CA 92093-0112, USA
Interests: high-dimensional time series; high-dimensional significance testing; change-point detection; high-order statistics, nonlinear time series; non-stationary time series; boostrapping and subsampling; time-varying network; random graphs

Special Issue Information

Dear Colleagues,

Time series data are becoming increasingly prevalent across various fields, such as finance, economics, engineering, biology, neuroscience, healthcare, and more. The statistical analysis of time series faces numerous challenges that complicate accurate data interpretation and forecasting. One primary issue is dealing with potentially non-Gaussian, non-linear, non-stationary, or high-dimensional data with complex dependence structures. Analyzing and understanding such complex data is essential because it can provide insights into patterns, trends, and relationships that may not be apparent with simpler dependence structures. Traditional theories and methodologies often prove inadequate for modern time series analysis. These challenges underscore the need for advanced statistical methods and computational tools to effectively analyze, interpret, and predict time series data. It is crucial to develop novel approaches for both time-domain and frequency-domain analysis to address these issues comprehensively.

This Special Issue is dedicated to reflecting recent advances in modern time series analysis from both theoretical and applied perspectives. By convening researchers and practitioners in these fields, we aim to highlight cutting-edge innovations and methodologies that address existing challenges.

Dr. Danna Zhang
Guest Editor

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Keywords

  • time series analysis
  • dependence structure
  • causality
  • dynamic models
  • non-stationarity
  • non-linearity
  • high dimensionality
  • robust analysis
  • prediction
  • resampling
  • statistical inference
  • hypothesis testing

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Published Papers (1 paper)

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Research

23 pages, 1212 KiB  
Article
A High-Dimensional Cramér–von Mises Test
by Danna Zhang and Mengyu Xu
Mathematics 2024, 12(22), 3467; https://doi.org/10.3390/math12223467 - 6 Nov 2024
Viewed by 666
Abstract
The Cramér–von Mises test provides a useful criterion for assessing goodness of fit in various problems. In this paper, we introduce a novel Cramér–von Mises-type test for testing distributions of high-dimensional continuous data. We establish an asymptotic theory for the proposed test statistics [...] Read more.
The Cramér–von Mises test provides a useful criterion for assessing goodness of fit in various problems. In this paper, we introduce a novel Cramér–von Mises-type test for testing distributions of high-dimensional continuous data. We establish an asymptotic theory for the proposed test statistics based on quadratic functions in high-dimensional stochastic processes. To estimate the limiting distribution of the test statistic, we propose two practical approaches: a plug-in calibration method and a subsampling method. Theoretical justifications are provided for both techniques. Numerical simulation also confirms the convergence of the proposed methods. Full article
(This article belongs to the Special Issue New Challenges in Time Series and Statistics)
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