  This paper introduces a new class of observation driven dynamic models. The
time evolving parameters are driven by innovations of copula form. The
resulting models can be made strictly stationary and the innovation term is
typically chosen to be Gaussian. The innovations are formed by applying a
copula approach for the conditional score function which has close connections
the existing literature on GAS models. This new method provides a unified
framework for observation-driven models allowing the likelihood to be
explicitly computed using the prediction decomposition. The approach may be
used for multiple lag structures and for multivariate models. Strict
stationarity can be easily imposed upon the models making the invariant
properties simple to ascertain. This property also has advantages for
specifying the initial conditions needed for maximum likelihood estimation. One
step and multi-period forecasting is straight-forward and the forecasting
density is either in closed form or a simple mixture over a univariate
component. The approach is very general and the illustrations focus on
volatility models and duration models. We illustrate the performance of the
modelling approach for both univariate and multivariate volatility models.
