Integrated VAR model with multivariate stochastic volatility and heavy-tailed errors - Cruz Torres, Cristian Andres (2026)
Vector autoregressive (VAR) models are used to capture the dynamic relationships among multivariate time series. On the other hand, multivariate stochastic volatility (MSV) models allow modeling the variance as it changes over time. Student’s t-distribution is used to model extreme values in time series. Therefore, this article proposes the integration of a VAR model, an MSV model, and a Student’s t-distribution (VAR-MSV-t). The selection of the most appropriate VAR-MSV-t order is carried out using the Deviance Information Criterion (DIC). Formulas are presented to estimate the Mardia skewness and the Koziol kurtosis of the model. The model is applied to three key macroeconomic variables for the United States. The S&P 500 stock market index is added, and the results are interpreted. Parameter estimation is carried out using Markov chain Monte Carlo (MCMC) methods. The results indicate that the model effectively captures the dynamic relationships, time-varying variance, and extreme magnitude values.