This thesis provides some theoretical and practical statistical inference tools for multivariate stochastic processes to better understand the behaviours and properties present in the data. In particular, we focus on the modelling of graphs,
that is a family of nodes linked together by a collection of edges, and extreme values, that
are values above a high threshold to have their own dynamics compared to the typical
behaviour of the process. We develop an ensemble of statistical models, statistical inference methods and their
asymptotic study to ensure the good behaviour of estimation schemes in a wide variety of
settings. We also devote a chapter to the formulation of a methodology based on pre-existing
theory to unveil the causal dependency structure behind high-impact events.