Large Vector Autoregressions with Stochastic Volatility and Flexible Priors

The original algorithm contained a mistake that meant the conditional distributions used for the VAR’s coefficients were missing a piece of information. We propose a new algorithm that uses the same factorization but includes the missing term. The new, correct algorithm has the same computational complexity as the old, incorrect one (i.e., O(N4)), and therefore it still allows the estimation of large VARs.

Recent research has shown that a reliable vector autoregressive model (VAR) for forecasting and structural analysis of macroeconomic data requires a large set of variables and modeling time variation in their volatilities. Yet, there are no papers jointly allowing for stochastic volatilities and large datasets, due to computational complexity. Moreover, homoskedastic VAR models for large datasets so far restrict substantially the allowed prior distributions on the parameters. In this paper we propose a new Bayesian estimation procedure for (possibly very large) VARs featuring time varying volatilities and general priors. This is important both for reduced form applications, such as forecasting, and for more structural applications, such as computing response functions to structural shocks. We show that indeed empirically the new estimation procedure performs very well for both tasks.