Detecting causal relations in time series with the new cross Markov Matrix technique

Nowadays, scientists are increasingly asked to investigate problems, which require the analysis of irregular, chaotic, non-stationary and corrupted time series. Assessing the causal relations between such signals is particularly challenging and, in many instances, interventions and experiments are impossible or impractical. The present work is a contribution to the development of indicators to quantify the mutual influences between time series. The criterion is called Cross Markov Matrix and belongs to the strand of techniques based on the conversion of time series into complex networks and the subsequent analysis of their topological properties. The proposed indicator is quite competitive with the available tools and can complement them very effectively. Indeed, all techniques have their strong and weak points and therefore corroborating the conclusions with mathematically independent methods is a recommended practice. The properties of the Cross Markov Matrix have been investigated with the help of a systematic series of numerical tests using synthetic data. The potential of the approach is then substantiated by the analysis of various real-life examples, ranging from environmental and global climate problems to the mutual influence between media coverage of Brexit and the pound-euro exchange rate.