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Semi-Automated Analysis of Peak Amplitude and Latency for Auditory Brainstem Response Waveforms Using R
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Elastic statistical analysis of interval-valued time series.

Honggang Zhang1, Jingyong Su1, Linlin Tang1

  • 1School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, People's Republic of China.

Journal of Applied Statistics
|December 19, 2022
PubMed
Summary

This study introduces a novel phase-amplitude separation method for analyzing interval-valued time series. The technique effectively models and clusters data across various scientific fields, including finance and meteorology.

Keywords:
Time warpingelastic shape analysisinterval-valued time series

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Area of Science:

  • Statistics
  • Data Analysis
  • Time Series Analysis

Background:

  • Statistical analysis of interval-valued time series data presents unique challenges.
  • Existing methods often struggle to capture both horizontal (phase) and vertical (amplitude) variability inherent in such data.
  • The need for robust methods to analyze and model data with inherent uncertainty is critical across scientific domains.

Purpose of the Study:

  • To develop a novel phase-amplitude separation method for interval-valued time series.
  • To enable effective registration, summarization, analysis, and modeling of multiple interval-valued time series.
  • To facilitate shape clustering of interval-valued time series data.

Main Methods:

  • Viewing interval-valued time series as elements of a function (Hilbert) space with a Riemannian structure.
  • Employing a metric-based alignment solution to separate phase and amplitude variability.
  • Mapping intervals to points in a specific space and utilizing elastic shape analysis techniques, including Principal Component Analysis (PCA), for curve analysis.

Main Results:

  • The proposed phase-amplitude separation method provides a new approach to PCA and modeling for interval-valued time series.
  • The framework enables effective shape clustering of interval-valued time series.
  • Successful application to diverse fields such as finance, meteorology, and physiology, demonstrating effectiveness and uncovering underlying data patterns.

Conclusions:

  • The developed phase-amplitude separation method is effective for statistical analysis of interval-valued time series.
  • The approach offers a powerful tool for data modeling, clustering, and pattern discovery in various scientific applications.
  • The method's applicability extends to point-valued time series, broadening its utility.