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Least-squares change-point estimation for the telegraph process observed at discrete times

2010; Taylor & Francis; Volume: 45; Issue: 4 Linguagem: Inglês

10.1080/02331881003769022

1029-4910

Alessandro De Gregorio, Stefano M. Iacus,

Stochastic processes and financial applications

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 a homogeneous Poisson process with rate λ>0. In this paper, we consider a change-point estimation problem for the rate of the underlying Poisson process by means of the least-squares method under the hypothesis of discrete-time sampling. Consistency, rate of convergence and distributional results for the change-point estimator are obtained under both fixed and random sampling. An application to real data is presented.