Forecasting with Bayesian vector autoregressive models : comparison of direct and iterated multistep methods

Purpose - The paper compares multi-period forecasting performances by direct and iterated method using Bayesian vector autoregressive (VAR) models. Design/methodology/approach - The paper adopts Bayesian VAR models with three different priors - independent Normal-Wishart prior, the Minnesota prior and the stochastic search variable selection (SSVS). Monte Carlo simulations are conducted to compare forecasting performances. An empirical study using US macroeconomic data are shown as an illustration. Findings - In theory direct forecasts are more efficient asymptotically and more robust to model misspecification than iterated forecasts, and iterated forecasts tend to bias but more efficient if the one-period ahead model is correctly specified. From the results of the Monte Carlo simulations, iterated forecasts tend to outperform direct forecasts, particularly with longer lag model and with longer forecast horizons. Implementing SSVS prior generally improves forecasting performance over unrestricted VAR model for either nonstationary or stationary data. Originality/value - The paper finds that iterated forecasts using model with the SSVS prior generally best outperform, suggesting that the SSVS restrictions on insignificant parameters alleviates over-parameterized problem of VAR in one-step ahead forecast and thus offers an appreciable improvement in forecast performance of iterated forecasts.