Bayesian automatic parameter estimation of Threshold Autoregressive (TAR) models using Markov Chain Monte Carlo (MCMC)

In nonlinear time series analysis a Threshold Autoregressive model (TAR) is considered as an approximation to a Nonlinear autoregressive process(NLAR). A TAR model is a piece-wise linear model over the state space. It is linear in the space of the thresholds. In this article we confine our studies to a class of TAR models which is called Self-Exciting Threshold Autoregressive (SETAR). The first step in fitting a SETAR model to. a data-set is to decide the number of regimes. The second step is to identify the delay, the threshold(thresholds) and the order of each regime. Our approach is to estimate automatically, the number of regimes, the delay, the threshold (thresholds), the order and parameters of each regime for this class of threshold models via a Bayesian approach using MCMC methods. Model selection is done through calculating mean of the root mean square error (MRMSE) of forecasts.