Change point estimation for the telegraph process observed at discrete times

TL;DR

This paper introduces a least squares method for estimating change points in the rate of the Poisson process underlying the telegraph model, providing theoretical guarantees and real data applications.

Contribution

It develops a novel change point estimation technique for the telegraph process's Poisson rate, with proven consistency and asymptotic properties.

Findings

Estimator is consistent and converges at a known rate.

Asymptotic distribution derived for the change point estimator.

Method applied successfully to real data.

Abstract

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity $+ v$ or $-v$. The changes of direction are governed by an homogeneous Poisson process with rate $\lambda >0.$ In this paper, we consider a change point estimation problem for the rate of the underlying Poisson process by means of least squares method. The consistency and the rate of convergence for the change point estimator are obtained and its asymptotic distribution is derived. Applications to real data are also presented.