Generalizing smooth transition autoregressions

We introduce a new time series model capable to parametrize the joint asymmetry in duration and length of cycles - the dynamic asymmetry - by using a particular generalization of the logistic function. The modelling strategy is discussed in detail, with particular emphasis on two different tests for the null of symmetric adjustment and three diagnostic tests, whose power properties are explored via Monte Carlo experiments. Four case studies in classical economic and biological real datasets illustrate the versatility of the new model in different fields. In all the cases, the dynamic asymmetry in the cycle is efficiently detected and modelled. Finally, a rolling forecasting exercise is applied to the resulting estimates. Our model beats linear and conventional nonlinear competitors in point forecasting, while this superiority becomes less evident in density forecasting, specially when relying on robust measures.