Using Density Forecast for Growth-at-Risk to Improve Mean Forecast of GDP Growth in Korea

In this paper, we study how we may use density forecasts to improve point forecasts for the Korean GDP growth rates during the period from 2013:Q3 to 2022:Q1. Although the time span under investigation is much shorter than desired, our conclusions are clear. Density forecasts improve point forecasts, as long as they are effectively approximated and represented as finite dimensional vectors by appropriately chosen functional bases. However, they may only be used to adjust point forecasts. Combining them with point forecasts to define weighted mean forecasts does not yield any meaningful improvement. The functional bases we use for our baseline approach are the leading functional principal components, which by construction most efficiently extract the variations in density forecasts over time. To disentangle the effects of the mean and other aspects of density forecasts, however, we also use the functional basis, which designates, as the leading factor, the mean factor that captures the temporal changes in the mean of density forecasts. Especially with the use of this functional basis, we see a drastic increase in the precision of point forecasts for the Korean GDP growth rates. In fact, the mean squared error of point forecasts decreases by more than 33%, if they are adjusted by density forecasts with our functional basis including the mean factor.