Estimating Time-Varying Networks for High-Dimensional Time Series

Jia Chen, Degui Li, Yuning Li and Oliver Linton

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

Abstract: We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over time. Two types of time-varying graphs are investigated: one containing directed edges of Granger causality linkages, and the other containing undirected edges of partial correlation linkages. Under the sparse structural assumption, we propose a penalised local linear method with time-varying weighted group LASSO to jointly estimate the transition matrices and identify their significant entries, and a time-varying CLIME method to estimate the precision matrices. The estimated transition and precision matrices are then used to determine the time-varying network structures. Under some mild conditions, we derive the theoretical properties of the proposed estimates including the consistency and oracle properties. In addition, we extend the methodology and theory to cover highly-correlated large-scale time series, for which the sparsity assumption becomes invalid and we allow for common factors before estimating the factor-adjusted time-varying networks. We provide extensive simulation studies and an empirical application to a large U.S. macroeconomic dataset to illustrate the finite-sample performance of our methods.

Keywords: CLIME; Factor model; Granger causality; lasso; local linear smoothing; partial correlation; time-varying network; VAR (search for similar items in EconPapers)
JEL-codes: C13 C14 C32 C38 (search for similar items in EconPapers)
Date: 2022-12-14
New Economics Papers: this item is included in nep-ecm and nep-ets
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https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe2273.pdf

Related works:
Working Paper: Estimating Time-Varying Networks for High-Dimensional Time Series (2023)
Working Paper: Estimating Time-Varying Networks for High-Dimensional Time Series (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:2273

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