With the aim of modelling key stylized features of observational series from finance and turbulence a number of stochastic processes with normal inverse Gaussian marginals and various types of dependence structures are discussed. Ornstein - Uhlenbeck type processes, superpositions of such...

Test statistics that are suitable for testing composite hypotheses are typically non-pivotal, and conservative bounds are commonly used to test composite hypotheses. In this paper, we propose a testing procedure for composite hypotheses that incorporates additional sample information. This...