Following the definition of systemic risk by the Financial Stability Board, the International Monetary Fund and the Bank for International Settlements, this paper proposes a method able to simultaneously address the two dimensions in which this risk materializes: namely the cross-sectional and the time dimension. The method is based on the W-TOPHITS algorithm, that exploits the connectivity information of an evolving network, and decomposes its tensor representation as the outer product of three vectors: borrowing, lending and time scores. These vectors can be interpreted as indices of the systemic importance of borrowing and lending associated with each financial institution and of the systemic importance associated with each period, coherently with the realization of the whole network in that period. The time score, being able to simultaneously consider the temporal distribution of the whole traded volume over time as well as the spatial distribution of the transactions between players in each period, turns out to be a useful Early Warning Signal of the financial crisis. The W-TOPHITS is tested on the e-MID interbank market dataset and on the BIS consolidated banking statistics with the aim of discovering Systemically Important Financial Institutions and to show how the time score is able to signal a change in the bipartite network of borrowers and lenders that heralds the fall of the traded volume that occurred during the 2007/2009 financial crisis.
Systemic Risk Tensor Early Warning Signals Evolving Networks