The asymmetric threshold model ASETAR(2,1,1)

In this paper we present a generalization of the Self-exciting threshold autoregressive (SETAR) model introduced by Tong and Lim (1980). In the SETAR model the system works in different regimes in each of which a suitable linear model approximates the true behaviour of the system. The system switches between two regimes with regard to the value assumed by a delayed variable compared with the threshold. The generalization that we introduce in this paper is to consider the possible presence of asymmetric switching rule, that is, the value of the threshold depend on the regime in which the system is at time t −d. In particular we present the asymetric threshold autoregressive model ASETAR(2;1,1). For this model the thresholds needed to define the switching rule are two: the first drives the system from regime 1 to regime 2 and the second drives the passage from regimes 2 to 1. For this model we propose an iterative procedure to estimate the parameters and present it applyed to simulated time series.