Ordinal pattern-based change point detection

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.