Sparsistent filtering of comovement networks from high-dimensional data

TL;DR

This paper introduces a spectral-based network filtering technique for high-dimensional dynamical systems, enabling effective sparsification while maintaining spectral properties, with applications to financial covariance networks.

Contribution

The novel spectral filtering method differs from topological filters by focusing on spectral properties, providing a tunable approach for sparsity and consistency in high-dimensional data.

Findings

The filter can interpolate between no filtering and maximal sparsity.

It achieves spectral closeness to linear shrinkage estimators.

Applied to financial data, it successfully extracts key subnetworks.

Abstract

Network filtering is an important form of dimension reduction to isolate the core constituents of large and interconnected complex systems. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior of the constituent nodes, exploiting their spectral properties. As opposed to the well known network filters that rely on preserving key topological properties of the realized network, our method treats the spectrum as the fundamental object and preserves spectral properties. Applying asymptotic theory for high dimensional data for the filter, we show that it can be tuned to interpolate between zero filtering to maximal filtering that induces sparsity and consistency while having the least spectral distance from a linear shrinkage estimator. We apply our proposed filter to covariance networks constructed from financial data, to extract the key subnetwork embedded in the full sample network.