We represent affine sub-manifolds of exponential family distributions as minimum relative entropy sub-manifolds. With such representation we derive analytical formulas for the inference from partial information on expectations and covariances of multivariate normal distributions; and we improve...

The Normal Inverse Gaussian (NIG) distribution recently introduced by Barndorff-Nielsen (1997) is a promising alternative for modelling financial data exhibiting skewness and fat tails. In this paper we explore the Bayesian estimation of NIG-parameters by Markov Chain Monte Carlo Methods. --...

We propose a new score-driven model to capture the time-varying volatility and tail behavior of realized kernels. We assume realized kernels follow an F distribution with two time-varying degrees-of-freedom parameters, accounting for the Vol-of-Vol and the tail shape of the realized kernel...