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Abstract
In this work, we present HMMLVis, an original visualization tool for multivariate Granger causal inference. More precisely, for heterogeneous Granger causality to infer causal relationships in time-series following an exponential distribution. HMMLVis is easy to use and can be applied in any scientific discipline exploring time series and their relationships. In this paper, we focus on climatological and meteorological applications. The visualization tool is demonstrated on different types of applications related to meteorological events on the upper/lower tails of the respective distributions using a renewable energy (wind, PV), air pollution, and the EUMETNET postprocessing benchmark data set (EUPPBench) and different temporal horizons. We demonstrate that the HMMLVis method and visualization depicts the known causal and detects causal relations in the temporal dependencies which are additional important information for the respective cases. We believe that HMMVis as an interpretable visualization tool will serve climatologists or meteorologists and in this way it will contribute to knowledge discovery in these scientific fields.

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