Network Modeling of Large-scale Time Series with Cumulative Impulse Response Functions

Network modeling of multivariate time series has emerged as an useful framework for understanding interactions amongst the component of a dynamical system in many areas of biological and social sciences. We develop a method to construct sparse, weighted, directed network where each edge captures how a shock to one component dynamically manifests in the other component using cumulative impulse response functions (cIRF). This is in sharp contrast with existing works, where network edges primarily capture in some form the Granger-causal effects (lead-lag association) among the component time series, and rely on a parsimonious vector autoregressive (VAR) representation of the system. Building upon our previous work on large-scale vector autoregressive moving averages (VARMA), we develop an iterative procedure for estimating cIRF. Using simulation experiments, we show that when the data generating process has a sparse vector moving average (VMA) representation, our method outperforms competing alternatives. We also prove that our algorithm, restricted to any finite number of iterations, consistently estimates impulse responses under high-dimensional asymptotics. Finally, we use our method to construct financial networks from realized volatilities of stock prices before, during and after the US financial crisis of 2007-09.