Evolutionary computational approach in TAR model estimation

The well-known SETAR model introduced by Tong belongs to the wide class of TAR models that may be specified in several different ways. Here we propose to consider the delay parameter as endogenous, that is we make it to depend on both the past value and the specific past regime of the series. In particular we consider a system that switches between two regimes, each of which is a linear autoregressive of order p, with respect of the value assumed by a delayed self--variable compared with an asymmetric threshold; the peculiarity is that the switching rule also depends on the regime in which the system lies at time t-d. In this work we consider two identification procedures: the first one follows the classical estimation for SETAR models, the second one proposes to estimate this model using the Particle Swarm Optimization technique.