Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

2007/12/12

15:20-16:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Stefano IACUS (Department of Economics, Business and Statistics, University of Milan)
Inference problems for the telegraph process observed at discrete times
[ Abstract ]
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.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/12.html