Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability ofevents in the future. Discovery of the underlying influence network among the dimensions of multidimensional temporal processes is of high importance in disciplines wherea high-frequency data is to model, e.g. in financial data or in seismological data. This paper approaches the problem of learning Granger-causal network in multidimensional Hawkes processes. We formulate this problem as a model selection task in which we follow the minimum description length (MDL) principle. Moreover, we propose a general algorithm for MDL-based inference using a Monte-Carlo method and we use it for our causal discovery problem. We compare our algorithm with the state-of-the-art baseline methods on synthetic and real-world financial data. The synthetic experiments demonstrate superiority of our method in causal graph discovery compared to the baseline methods with respect to the size of the data. The results of experiments with the G-7 bonds price data are consistent with the experts’ knowledge.

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