Date/heure
26 septembre 2024
09:15 - 10:15
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Paolo Pigato (Roma)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
In this work, we define a multivariate version of the fractional Ornstein-Uhlenbeck process, i.e. the solution to a stochastic differential equation with affine drift and constant volatility, driven by a fractional Brownian motion. The resulting process is a multivariate stationary and ergodic process, with smoothness/regularity degree that can be different in each component. Such process has a richer correlation structure than that of the classical diffusive case, in the sense that the correlation between i-th and j-th components is ruled by two parameters. We propose two types of estimator for these parameters, of which we study analytically the long time asymptotic behavior, and the finite sample behavior on numerical simulations. Finally, motivated by rough volatility modelling, we apply this framework to realized volatility time series.
This is a joint work with Ranieri Dugo and Giacomo Giorgio, based on arxiv preprint 2408.03051.