We develop a new simultaneous time series model for volatility and dependence in daily financial return series that are subject to long memory (fractionally integrated) dynamics and heavy-tailed densities. Our new multivariate model accounts for typical empirical features in financial time series while being robust to outliers or jumps in the data. In our empirical study for daily return series of four Dow Jones equities, we find that the degree of memory in the volatilities is similar, while the degree of memory in correlations between the series varies significantly. The forecasts from our daily model are compared with high-frequency realized volatility and dependence measures. The overall performance of the new model is better than that of several well-known competing benchmark models.