Engle's ARCH model is extended to permit parametric specifications for
conditional dependence beyond the mean and variance. The suggestion i
s to model the conditional density with a small number of ''parameters
,'' and then model these parameters as functions of the conditioning i
nformation. This method is applied to two data sets. The first applica
tion is to the monthly excess holding yield on U.S. Treasury securitie
s, where the conditional density used is a student's t distribution. T
he second application is to the U.S. Dollar/Swiss Franc exchange rate,
using a new ''skewed student t'' conditional distribution.