Abstract:
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The impulse response function characterizes how components interact within multivariate time series and its study is motivated by many applications, including macroeconmics, finance, and signal processing. We focus on large-scale networks or graphical models of time series where regularized estimation of vector autoregression (VAR) and Granger causal (direct lagged effect) models have been extensively studied recently. The impulse response function (IRF) has received relatively little attention and is not well understood in high dimension; however, its inherent ability to capture ``shock propagation" directly makes it an essential tool in many applications. Transforming regularized VAR estimates into forecast error variance decompositions or IRFs has many limitations or drawbacks in high dimension. We propose regularized estimation of the IRF through assuming sparsity in shock propagation and directly identify the most important channels of shock propagation. We conduct inference based on debiasing and our contemporaneous covariance estimation allows for a more generalized IRF. We illustrate our approach on various empirical examples.
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