Nonlinear stochastic trends

A nonlinear growth process has its change equal to a positive function of the lagged series plus an innovation whose variance depends on the lagged series. If the innovations were identically zero the resulting deterministic trends take a wide variety of shapes. The balance between growth in mean and variance to guarantee eventual growth of the process is determined, the relationship between stochastic and deterministic trends found, parametric and nonparametric estimates of the functions considered and applications analysed. The natural bivariate generalization is found to produce a form of cointegration and a nonlinear error-correction model.