Forecasting with Vector Autoregressions Using Bayesian Variable Selection Methods: Comparison of Direct and Iterated Methods

This paper compares multi-period forecasting performances by direct and iterated method using a Bayesian vector autoregressions with the stochastic search variable selection (SSVS) priors. The forecasting performances are evaluated using the artificially generated data with both nonstationary and stationary process. 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. As an illustration, US macroeconomic data sets with three variables are examined to compare iterated and direct forecasts using the unrestricted VAR model and the SSVS VAR model. Overall, iterated forecasts using model with the SSVS 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