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 +ν or -ν. 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 discretetime 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.
Least-squares change-point estimation for the telegraph process observed at discrete times / A. De Gregorio, S.M. Iacus. - In: STATISTICS. - ISSN 0233-1888. - 45:4(2011), pp. 349-359. [10.1080/02331881003769022]
Least-squares change-point estimation for the telegraph process observed at discrete times
S.M. Iacus
2011
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 +ν or -ν. 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 discretetime 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.File | Dimensione | Formato | |
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