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).