Ordinal Patterns Based Change Points Detection

TL;DR

This paper introduces a method using ordinal patterns to detect change points in time series, proving asymptotic normality for linear increment processes and demonstrating its effectiveness in identifying distribution shifts.

Contribution

It establishes the asymptotic normality of ordinal pattern frequencies for linear increment time series and applies this to change point detection.

Findings

Proves asymptotic normality of ordinal pattern frequencies

Demonstrates change point detection in distribution shifts

Provides theoretical foundation for ordinal pattern analysis

Abstract

The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of the time series. In this work, we prove the asymptotic normality of the relative frequency of ordinal patterns for time series with linear increments. Moreover, we apply ordinal patterns to detect changes in the distribution of a time series.