Multiscale Dynamic Dependence Estimation over Networks

In numerous scientific and industrial settings, observed multivariate time series are often nonstationary in nature, i.e., comprise data whose second order properties vary over time.

An additional feature of many modern datasets is that the cross-dependencies of such series are structured by an underlying network, giving rise to complex interactions between temporal dynamics and network topology.

In this article we propose Locally Stationary Wavelet processes on Networks (Net-LSW), a new framework for modelling multiscale, time-varying dependencies that explicitly incorporates the network structure.

Unlike traditional multivariate approaches, the Net-LSW process encodes the graph directly in the covariance structure of the process's random increments.

We also introduce the concept of the local partial correlation graph, which connects edges in the graph to non-zero entries in the time- and scale-dependent dependence structure of a nonstationary process.

For inference on the local cross-nodal (partial) dependence, we develop a novel subprocess-based estimation scheme and establish its desirable consistency properties.

Simulation studies further demonstrate that the proposed framework accurately recovers evolving dependence structures whilst respecting the underlying graph topology.

Finally, we apply our framework to daily stock price volatilities across a global bank network, demonstrating its ability to capture multiscale, highly nonstationary dependencies and identify time-varying systemic shifts during major financial shocks, including Brexit and the COVID-19 pandemic.