  Risk evaluation is a forecast, and its validity must be backtested.
Probability distribution forecasts are used in this work and allow for more
powerful validations compared to point forecasts. Our aim is to use bivariate
copulas in order to characterize the in-sample copulas and to validate
out-of-sample a bivariate forecast. For both set-ups, probability integral
transforms (PIT) and Rosenblatt transforms are used to map the problem into an
independent copula. For this simple copula, statistical tests can be applied to
validate the choice of the in-sample copula or the validity of the bivariate
forecast. The salient results are that a Student copula describes well the
dependencies between financial time series (regardless of the correlation), and
that the bivariate forecasts provided by a risk methodology based on historical
innovations performs correctly out-of-sample. A prerequisite is to remove the
heteroskedasticity in order to have stationary time series, in this work a
long-memory ARCH volatility model is used.
