This paper collects in one place a comprehensive theory of stochastic realization for continuous time stationary Gaussian vector processes which in various pieces has appeared in a number of our earlier papers. It begins with an abstract state space theory, based on the concept of splitting subspace. These results are then carried over to the spectral domain and described in terms of Hardy func...

Developing valid frequency domain bootstrap procedures for integrated periodogram statistics multivariate time series is a challenging problem. This mainly due to the fact that distribution of such depends on fourth-order moment structure underlying process in nearly every scenario. Exceptions are some very special cases like nonparametric estimators spectral density matrix or Gaussian series. ...

We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Lévy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences. 1. Introduction. In a fundamental paper [9], Rosi´nski revealed the hidden structure of stationary symmetric α-stable (SαS) processes. Namely, he proved t...