Empirical relationship between stocks' cross-correlation and stocks' volatility clustering

In this paper we discuss univariate and multivariate statistical properties of volatility with the aim of understanding how these two aspects are interrelated. Specifically, we investigate the relationship between the cross-correlation among stocks' volatilities and the volatility clustering. Volatility clustering is related to the memory property of the volatility time-series and therefore to its predictability. Our results show that there exists a relationship between the level of predictability of any volatility time-series and the extent of its inter-dependence with other assets. In all considered cases, the more the asset is linked to other assets, the more its volatility retains memory of its past behavior. We also discuss the impact of these findings on the network properties of the system. We show that when the system involves many strongly autocorrelated volatilities the minimum spanning tree gets less structured, showing a large cluster of nodes centered around a hub with large degree. As a by-product, we also show that the way the volatility autocorrelation function decays is only marginally related to the decay in the probability distribution function. (paper)