Evaluating Density Forecasts via the Copula Approach
Working Paper No. 02-W25R
Xiaohong Chen and Yanqin Fan
ABSTRACT [article]
In this paper, we develop a general approach for constructing simple tests for the correct density forecasts, or equivalently,
for i.i.d. uniformity of appropriately transformed random
variables. It is based on nesting a series of i.i.d. uniform random
variables into a class of copula-based stationary Markov processes.
As such, it can be used to test for i.i.d. uniformity against
alternative processes that exhibit a wide variety of marginal
properties and temporal dependence properties, including skewed and
fat-tailed marginal distributions, asymmetric dependence, and
positive tail dependence. In addition, we develop tests for the
dependence structure of the forecasting model that are robust to
possible misspecification of the marginal distribution.