Bayesian test for asymmetry and nonstationarity in MTAR model with possibly incomplete data

We propose an easy and efficient Bayesian test procedure for asymmetry and nonstationarity in momentum threshold autoregressive model with possibly incomplete data. Estimation of parameters and missing observations is done by using a Markov chain Monte Carlo (MCMC) method. Testing for asymmetry and nonstationarity is done via test of multiple hypotheses representing various types of symmetry/asymmetry and stationarity/nonstationarity. This allows simultaneous consideration of parameters relevant to asymmetry and nonstationarity of the model, and also enables us to find the sources of asymmetry and nonstationarity when they exist. Posterior probabilities of the hypotheses are easily computed by using MCMC outputs under the full model, with almost no extra cost. We apply the proposed method to a set of Korea unemployment rate data.