Forecasting based on a multivariate autoregressive threshold model (MTAR) with a multivariate Student’s t error distribution: A Bayesian approach

This article presents a Bayesian method for obtaining forecasts based on a multivariate threshold autoregressive (MTAR) model with a multivariate Student’s t error distribution. We derive the Bayesian predictive distribution, which incorporates uncertainty about the true values of the MTAR model parameters. The proposed procedure involves drawing samples from the predictive distribution to obtain point forecasts and prediction intervals for each univariate component of the multivariate process of interest. Although the model accounts for the multivariate nature of the data, the prediction intervals are constructed individually for each variable. We verify the performance of the proposed algorithm through a simulation study based on three models, calculating the percentage of times the true values of each component of the output process fall within the 95% individual prediction intervals of the predictive distribution. Additionally, we present an application to a set of financial time series, where forecasts of the returns of the Bovespa and Colcap indexes are obtained using the returns of the Standard and Poor’s 500 index as the threshold variable.