German Title: Modellierung und Vorhersage von Realisierten Kovarianzmatrizen

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Abstract

In this thesis, we use observation-driven models for time-series of daily RCs. That is, we assume a matrix-variate probability distribution for the daily RCs, whose parameters are updated based on the RC realizations from previous days.

In particular, Chapter 2 looks at different matrix-variate probability distributions for the RCs and their theoretical and empirical properties. Chapter 3 proposes a flexible observation-driven model to update all distribution-specific time-varying parameters, not just the expected value matrix as is done in the literature so far. Chapter 4 introduces an observation-driven updating mechanism that is applicable to high-dimensional time-series of RCs. Each of these three chapters is a self-contained paper.