Traditional multivariate statistical methods, which are often used to monitor stationary processes, not applicable nonstationary processes. Cointegration analysis (CA) is considered an effective method deal with variables. If there a cointegration relationship among the series in system, it indicates that stable long-term dynamic equilibrium exists these However, due complexity of modern indust...

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R and in some cases provide a full characterisation of the stationarity property. In particular, a full characterisation of stationary multivariate Brown–Resnick processes is given.

We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The main class of models explored is a novel class of stationary, first-order autoregressive (AR) processes on the cone of positive semi-definite matrices. Aspects of the theory and structure of these new models for multiv...