Multivariate Self-Exciting Threshold Autoregressive Modeling by Genetic Algorithms

Several nonlinear time series models have been proposed in the literature to explain various empirical nonlinear features of many observed financial and economic time series. One model that has gained much attention is the so-called self-exciting threshold autoregressive (SETAR) model. It has been found very effective for modeling and forecasting nonlinear time series in a wide range of application fields. Furthermore, SETAR model is able to capture nonlinear characteristics as limit cycles, jump resonance, and time irreversibility. In this work the attention is focused on a multivariate SETAR (MSETAR) model where each linear regime follows a vector autoregressive (VAR) process and the thresholds are multivariate. We propose a methodology based on genetic algorithms (GAs) for building MSETAR models. The GA is designed to estimate the structural parameters, i. e. to determine the appropriate number of regimes and find multivariate threshold parameters. The behavior of the proposed methodology has been observed on a simulation experiment involving three artificial data sets.