Improved Methods for Combining Point Forecasts for an Asymmetrically Distributed Variable

Many studies have found that combining forecasts improves predictive accuracy. An
often-used approach developed by Granger and Ramanathan (GR, 1984) utilises a
linear-Gaussian regression model to combine point forecasts. This paper generalises
their approach for an asymmetrically distributed target variable. Our copula point
forecast combination methodology involves fitting marginal distributions for the target
variable and the individual forecasts being combined; and then estimating the correlation
parameters capturing linear dependence between the target and the experts' predictions.
If the target variable and experts' predictions are individually Gaussian distributed, our
copula point combination reproduces the GR combination. We illustrate our methodology
with two applications examining quarterly forecasts for the Federal Funds rate and for
US output growth, respectively. The copula point combinations outperform the forecasts
from the individual experts in both applications, with gains in root mean squared forecast
error in the region of 40% for the Federal Funds rate and 4% for output growth relative to
the GR combination. The fitted marginal distribution for the interest rate exhibits strong
asymmetry.