A model-free test of the time-reversibility of climate change processes

TL;DR

This paper introduces a model-free statistical test for assessing the time-reversibility of climate change processes using copula spectrum analysis, providing a more accurate and assumption-free method compared to traditional model-based tests.

Contribution

The paper presents a novel, model-free test for time-reversibility in time series, based on copula spectrum characterization, applicable to climate data analysis.

Findings

The test accurately detects time-reversibility in simulated data.

Application to climate data reveals non-reversibility in real-world processes.

The method outperforms existing model-based tests in reliability.

Abstract

Time-reversibility is a crucial feature of many time series models, while time-irreversibility is the rule rather than the exception in real-life data. Testing the null hypothesis of time-reversibilty, therefore, should be an important step preliminary to the identification and estimation of most traditional time-series models. Existing procedures, however, mostly consist of testing necessary but not sufficient conditions, leading to under-rejection, or sufficient but non-necessary ones, which leads to over-rejection. Moreover, they generally are model-besed. In contrast, the copula spectrum studied by Goto et al. ($\textit{Ann. Statist.}$ 2022, $\textbf{50}$: 3563--3591) allows for a model-free necessary and sufficient time-reversibility condition. A test based on this copula-spectrum-based characterization has been proposed by authors. This paper illustrates the performance of this test, with an illustration in the analysis of climatic data.