Nonlinear Persistence and Copersistence.

In a nonlinear framework the magnitude of temporal dependence may depend on the transformation applied to time series. The aim of this paper is to examine in detail various forms of persistence and the corresponding transformations. For multivariate series the persistence analysis is used to reveal nonlinear comovements between the components, called the copersistence directions (or cointegration directions in the nonstationary case). In general, there exists a multiplicity of such direction, causing an identification problem.