Bayesian Vector Heterogeneous Autoregressive Modeling

Abstract

The Bayesian vector autoregressive (BVAR) model with the Minnesota prior proposed by Litterman (1986) has been very successful in multivariate time series modeling, providing better forecasting performance. However, the conventional Minnesota prior for BVAR depends only on the latest lag; in turn, it is not suitable for multivariate long memory time series forecasting. This study extends BVAR to vector heterogeneous autoregressive (VHAR) structure to accommodate long-term persistence and impose priors on distant lags as well. Our proposed Bayesian VHAR (BVHAR) models, the so-called BVHAR-S and BVHAR-L, are easy to implement by using the Normal-inverse-Wishart prior and added dummy variable approach of Bańbura et al. (2010). We further apply our models to nine CBOE Volatility Indices (VIXs).