- Abstract: To address the long run predictability puzzle and enable long run predictions, we introduce nonlinear dynamic models. In these models, observations are expressed as a nonlinear function of two key components: a stationary process representing the short term dynamics and an ultra long run (ULR) component. The ULR component is derived from an underlying stationary diffusion process through an “infinite” change of time unit, resulting in a stationary local-to-unity model. We outline the construction of suitable autocorrelation functions and the process of filtering the short run and ULR components. Additionally, we introduce an estimation approach for the dynamic model of both the short term and ULR components using pairwise likelihood methods. We also highlight the impossibility to get accurate long run predictions even with a large number of observations. This challenge is illustrated by a stochastic volatility-in-mean model.