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Beschreibung:
Point process models are used in a variety of applications to describe events that occur randomly in time. If real-world data reveal that the events arrive in clusters, a specific class of point processes, the self-exciting process, is often used to account for this behavior. In this work, we examine different point process models and focus on the application to intraday electricity market data. The contribution of this thesis is threefold. First, we propose a novel point process model to describe the arrival times of orders on the German intraday electricity market. Since the orders do not only arrive in clusters, but are affected by external influences as well, we enhance a self-exciting process with additional exogenous factors, such as the errors in wind or solar power forecasts. Our empirical analysis implies that the self-exciting process with exogenous factors outperforms both purely self-exciting and purely exogenous models. Second, we examine point process models with an intensity that depends on an unobservable stochastic process. In this setting, the likelihood function has to be approximated to estimate the model parameters. To enable the application of gradient-based optimization algorithms, we use automatic differentiation to obtain exact derivatives. In a simulation study, we can show that gradient-based optimization algorithms combined with automatic differentiation speed up the estimation of model parameters compared to derivate-free approaches while preserving the quality of the solution. Third, we investigate a classification task for self-exciting processes. With the help of several machine learning algorithms, we try to separate the events that trigger a cluster from those remaining. Additionally, we propose a novel estimation approach for self-exciting processes that is based on the identified type of every event. In this approach, the parameters that are associated to the two possible event types are successively estimated in two steps. The results of a simulation study imply that the ...