Probabilistic Forecasting with Stationary VAR Models

Abstract

I use a set of vector autoregressive models to forecast some of the main macroeconomic variables in a wide range of countries. The goal is to provide some insight about different forecast accuracy measures in a probabilistic forecasting framework. The countries are selected based on their available data in the International Financial Statistics (IFS) database. The target variables are GDP, CPI and exchange rate growth in yearly, quarterly and monthly frequencies. I specify the model sets by using a list of potentially relevant variables from IFS database. The results are available up to four forecast horizons and for two different classes of forecast accuracy measures: The probabilistic class which contains linear, logarithmic, quadratic, Hyvarinen and continuous ranked probability score rules, and the non-probabilistic class which contains mean absolute and mean square error measures. The results show that the forecasts are sensitive to the choice of a forecast accuracy class, in sense of Hellinger distance. However, within each class, the choice is not critical. Among different probabilistic measures, the logarithmic and quadratic rules are more reliable in practice. The results also show that the forecast power of stationary multivariate models is higher than the univariate ones, for both probabilistic and non-probabilistic accuracy measures.