Change point analysis with irregular signals

TL;DR

This paper introduces a novel two-step method for detecting and estimating change points in signals that are highly irregular after the change, surpassing traditional assumptions of smoothness or piece-wise constancy.

Contribution

It proposes a new approach that effectively estimates change points in irregular signals and demonstrates an $ ext{O}_P(1)$ convergence rate under certain conditions.

Findings

Successfully identified the COVID-19 pandemic start date as December 8, 2019.

The method achieves a desirable convergence rate for change point estimation.

Applied to real-world COVID-19 data, validating its practical utility.

Abstract

This paper considers the problem of testing and estimation of change point where signals after the change point can be highly irregular, which departs from the existing literature that assumes signals after the change point to be piece-wise constant or vary smoothly. A two-step approach is proposed to effectively estimate the location of the change point. The first step consists of a preliminary estimation of the change point that allows us to obtain unknown parameters for the second step. In the second step we use a new procedure to determine the position of the change point. We show that, under suitable conditions, the desirable $\mathcal{O}_P(1)$ rate of convergence of the estimated change point can be obtained. We apply our method to analyze the Baidu search index of COVID-19 related symptoms and find 8~December 2019 to be the starting date of the COVID-19 pandemic.