Dynamic models using score copula innovations

Abstract

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.