The telegraph process {X(t), t>0}, has been introduced (see Goldstein, 1951) as an alternative model to the Brownian motion B(t). This process describes a motion of a particle on the real line which alternates its velocity, at Poissonian times, from +v to -v. The density of the distribution of the position of the particle at time t solves the hyperbolic differential equation called telegraph equation and hence the name of the process. Contrary to B(t) the process X(t) has finite variation and continuous and differentiable paths. At the same time it is mathematically challenging to handle. Several variation of this process have been recently introduced in the context of Finance.

In this talk we will discuss pseudo-likelihood and moment type estimators of the intensity of the Poisson process, from discrete time observations of standard telegraph process X(t). We also discuss the problem of change point estimation for the intensity of the underlying Poisson process and show the performance of this estimator on real data.