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Abstract:
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Spectral analysis of ?nancial comovement networks is a standard method to infer dynamics of the underlying ?nancial markets. The theory is well-developed when the asset price data has smaller number of time-series (p) than the number of data points in each time-series (n). However, the rapid expansion of the real-world ?nancial web necessitates an extension the domain of the network analysis to the case where the problem of high-dimensionality is acute, i.e. p > n. To this end, we develop a new spectral ?lter which generates sparsistent networks. Applying asymptotic theory of high-dimensional covariance matrix estimation, we show that the proposed method can be tuned to interpolate between zero ?ltering to maximal ?ltering that induces sparsity via thresholding, while having the least spectral distance from a consistent (non-)linear shrinkage estimator. We demonstrate the application of our proposed method by applying it to covariance networks constructed from high-dimensional ?nancial data, to extract core subnetworks embedded in full networks.
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