A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series

Abstract

“Iterated” multiperiod-ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas “direct” forecasts are made using a horizon-specific estimated model, where the dependent variable is the multiperiod ahead value being forecasted. Which approach is better is an empirical matter: in theory, iterated forecasts are more efficient if the one-period ahead model is correctly specified, but direct forecasts are more robust to model misspecification. This paper compares empirical iterated and direct forecasts from linear univariate and bivariate models by applying simulated out-of-sample methods to 170 U.S. monthly macroeconomic time series spanning 1959–2002. The iterated forecasts typically outperform the direct forecasts, particularly, if the models can select long-lag specifications. The relative performance of the iterated forecasts improves with the forecast horizon.