Modelling Asymmetric Behaviour in Time Series: Identification Through PSO

In this work we propose an estimation procedure of a specific TAR model in which the actual regime changes depending 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. The switching rule, which drives the process from one regime to another one, depends on the value assumed by a delayed variable compared with only one threshold, with the peculiarity that even the thresholds change according to the regime in which the system lies at time t -d. This allows the model to take into account the possible asymmetric behaviour typical of some financial time series. The identification procedure is based on the Particle Swarm Optimization technique.