Nonlinear persistence and copersistence

This chapter examines relationships between various forms of persistence in nonlinear transformations of stationary and nonstationary processes. We introduce the concept of persistence space that is used to define the degrees of persistence in univariate and multivariate time series. For illustration, we examine and compare persistence in a fractionally integrated process and in a beta mixture of AR(1) processes. We also propose the concept of persistence by trajectory that allows us to define nonlinear cointegration and discuss identification problems that arise in this context.