Change point estimation for the telegraph process observed at discrete times
Alessandro De Gregorio, Università di Milano, Italy
Stefano Iacus, Department of Economics, Business and Statistics, University of Milan, IT
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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.
SUGGESTED CITATION:
Alessandro De Gregorio and Stefano Iacus,
"Change point estimation for the telegraph process observed at discrete times"
(May 2007).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 23.
http://services.bepress.com/unimi/statistics/art23
Paper presented by A. De Gregorio, S.M. Iacus.
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