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Ordinal pattern-based change point detection.

Annika Betken1, Giorgio Micali1, Johannes Schmidt-Hieber1

  • 1Department of Applied Mathematics, University of Twente, 7522 NB Enschede, The Netherlands.

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Summary
This summary is machine-generated.

We analyzed time series using ordinal patterns to understand their properties. Our findings show these patterns can detect distribution changes in linear increment time series.

Keywords:
Change point detectionOrdinal patternsTurning rate

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Area of Science:

  • Time Series Analysis
  • Statistical Pattern Recognition

Background:

  • Ordinal patterns represent the spatial ordering of values within a time series segment.
  • The frequency of specific ordinal patterns offers insights into time series characteristics.

Purpose of the Study:

  • To prove the asymptotic normality of ordinal pattern frequencies in linear increment time series.
  • To demonstrate the application of ordinal patterns for detecting changes in time series distributions.

Main Methods:

  • Analysis of ordinal patterns in consecutive time series values.
  • Statistical methods to establish asymptotic normality for relative frequencies.
  • Application of ordinal pattern analysis for change point detection.

Main Results:

  • Asymptotic normality of the relative frequency of ordinal patterns is proven for linear increment time series.
  • Ordinal patterns effectively detect changes in the underlying time series distribution.

Conclusions:

  • The study validates a key statistical property of ordinal patterns in a specific time series class.
  • Ordinal pattern analysis is a viable tool for monitoring and detecting distributional shifts in time series data.