  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.
