Bayesian multi-regime smooth transition regression with ordered categorical variables

Multivariate time series are ubiquitous among a broad array of applications and often include both categorical and continuous series. Further, in many contexts, the continuous variable behaves nonlinearly conditional on a categorical time series. To accommodate the complexity of this structure, we propose a multi-regime smooth transition model where the transition variable is derived from the categorical time series and the degree of smoothness in transitioning between regimes is estimated from the data. The joint model for the continuous and ordinal time series is developed using a Bayesian hierarchical approach and thus, naturally, quantifies different sources of uncertainty. Additionally, we allow a general number of regimes in the smooth transition model and, for estimation, propose an efficient Markov chain Monte Carlo algorithm by blocking the parameters. Moreover, the model can be effectively used to draw inference on the behavior within and between regimes, as well as inference on regime probabilities. In order to demonstrate the frequentist properties of the proposed Bayesian estimators, we present the results of a comprehensive simulation study. Finally, we illustrate the utility of the proposed model through the analysis of two macroeconomic time series.