Résumé : Motivated from a changing market environment over time, we
consider high-dimensional data such as financial returns, generated by
a hidden Markov model which allows for switching between different
regimes or states. To get more stable estimates of the covariance
matrices of the different states, potentially driven by a number of
observations which is small compared to the dimension, we apply
shrinkage and combine it with an EM-type algorithm. The final
algorithm turns out to reproduce better estimates also for the
transition matrix. It results into a more stable and reliable filter
which allows for reconstructing the values of the hidden Markov chain.
In addition to a simulation study performed in this paper, we also
present a series of theoretical results which include a dimensionality
asymptotics and which provide the motivation for certain techniques
used in the algorithm.

Cet exposé se tiendra en salle C20-13, 20ème étage, Université
Paris 1, Centre Pierre Mendès-France, 90 rue de Tolbiac, 75013 Paris
(métro : Olympiades).