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Title: Probability distributions for realized covariance matrices Authors:  Michael Stollenwerk - Heidelberg University (Germany) [presenting]
Abstract: Realized covariance matrices (RCs) are an important input to assess the risks involved in different investment allocations and it is thus useful to model and forecast them. To this end, generalized autoregressive score (GAS) models are employed. These models are ideal for comparing different probability distributions in terms of their ability to model and forecast RCs, since the dynamic parameters of the conditional observation density are updated by incorporating the shape of the distribution itself (via the scaled score of the log-likelihood). A novel type of probability distribution is derived and compared to all other probability distributions so far applied to RCs in the literature. The necessary inputs for the GAS models (Fisher information matrix and score) are derived for all distributions. An in-sample fit comparison confirms previous results that ``fat-tailed'' distributions outperform others and shows that the novel distribution achieves the best fit. Out-of-sample forecasting comparisons will be done using different economically relevant loss functions.