SUMMARYWe propose a new dynamic copula model in which the parameter characterizing dependence follows an autoregressive process. As this model class includes the Gaussian copula with stochastic correlation process, it can be viewed as a generalization of multivariate stochastic volatility models. Despite the complexity of the model, the decoupling of marginals and dependence parameters facilitates estimation. We propose estimation in two steps, where first the parameters of the marginal distributions are estimated, and then those of the copula. Parameters of the latent processes (volatilities and dependence) are estimated using efficient importance sampling. We discuss goodness-of-fit tests and ways to forecast the dependence parameter. For two bivariate stock index series, we show that the proposed model outperforms standard competing models.

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We propose a model that can capture the typical features of multivariate extreme events observed in financial time series, namely clustering behavior in magnitudes and arrival times of multivariate extreme events, and time-varying dependence. The model is developed in the framework of the peaks-over-threshold approach in extreme value theory and relies on a Poisson process with selfexciting intensity. We discuss the properties of the model, treat its estimation, deal with testing goodness-of-fit, and develop a simulation algorithm. The model is applied to return data of two stock markets and four major European banks.