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Summary  Interconnectedness between stocks and firms plays a crucial role in the volatility contagion phenomena that characterize financial crises, and graphs are a natural tool in their analysis. We propose graphical methods for an analysis of volatility interconnections in the Standard & Poor's 100 data set during the period 2000–2013, which contains the 2007–2008 Great Financial Crisis. The challenges are twofold: first, volatilities are not directly observed and must be extracted from time series of stock returns; second, the observed series, with about 100 stocks, is high dimensional, and curse‐of‐dimensionality problems are to be faced. To overcome this double challenge, we propose a dynamic factor model methodology, decomposing the panel into a factor‐driven and an idiosyncratic component modelled as a sparse vector auto‐regressive model. The inversion of this auto‐regression, along with suitable identification constraints, produces networks in which, for a given horizon  h , the weight associated with edge ( i , j ) represents the  h ‐step‐ahead forecast error variance of variable  i  accounted for by variable  j 's innovations. Then, we show how those graphs yield an assessment of how  systemic  each firm is. They also demonstrate the prominent role of financial firms as sources of contagion during the 2007–2008 crisis.

A network analysis of the volatility of high dimensional financial series