Testing for Structural Breaks via Ordinal Pattern Dependence

TL;DR

This paper introduces a novel method for analyzing dependence between two time series using ordinal patterns, providing stable, transformation-invariant measures and a test for detecting changes in their dependence structure.

Contribution

It develops new ordinal pattern-based dependence measures, estimators, asymptotic distributions, and a structural break test, with validation through simulations and empirical data.

Findings

Ordinal pattern dependence effectively captures non-linear relationships.

The proposed test detects structural breaks in dependence structure.

Simulation studies confirm the robustness and accuracy of the methods.

Abstract

We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of the time series and robust against small perturbations or measurement errors. Ordinal pattern dependence can be characterized by four parameters. We propose estimators for these parameters, and we calculate their asymptotic distributions. Furthermore, we derive a test for structural breaks within the dependence structure. All results are supplemented by simulation studies and empirical examples. For three consecutive data points attaining different values, there are six possibilities how their values can be ordered. These possibilities are called ordinal patterns. Our first idea is simply to count the number of coincidences of patterns in both time series, and to compare this with the expected number in the case of independence. If we detect a lot of coincident patterns, this means that the up-and-down behavior is similar. Hence, our concept can be seen as a way to measure non-linear `correlation'. We show in the last section, how to generalize the concept in order to capture various other kinds of dependence.