Bayesian Analysis of Threshold Autoregressive Model with First Order Autoregressive Innovations

Abstract

Financial assets exhibit dramatic changes in behaviour. This work examined a two-regime Threshold autoregressive (TAR) models when the innovations follow a first-autoregressive order process. The Bayesian method is proposed to build in the linear first-order autoregressive process with identical distributed innovations. The practical usefulness of this method is demonstrated with simulated and real-life data using U.S.A quarterly real GDP as an example. In simulation experiments and real life example, an increase in first order process parameter, ρ value leads to better estimates in the proposed model. Also, the proposed model was compared with TAR model where the disturbance term does not exhibit regime switching. The proposed model performed well than the traditional TAR model using the simulated and real life data. An increase in first order process parameter, ρ will lead to better estimates and forecast. Hence, the proposed model performed well.