In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary...

In thiswork,we extend some parameters built on a probability distribution introduced before to the casewhere the proximity between real numbers is measured by using a Bregman divergence. This leads to the definition of the Bregman superquantile (thatwe can connect with severalworks in economy, see for example [18] or [9]). Axioms of a coherent measure of risk discussed previously (see [31] or [3]) are studied in the case of Bregman superquantile. Furthermore,we deal with asymptotic properties of...