High-Dimensional VARs with Common Factors

Ke Miao, Peter Phillips and Liangjun Su ()
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Ke Miao: School of Economics, Fudan University

No 2252, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper studies high-dimensional vector autoregressions (VARs) augmented with common factors that allow for strong cross section dependence. Models of this type provide a convenient mechanism for accommodating the interconnectedness and temporal co-variability that are often present in large dimensional systems. We propose an '1-nuclear-norm regularized estimator and derive non-asymptotic upper bounds for the estimation errors as well as large sample asymptotics for the estimates. A singular value thresholding procedure is used to determine the correct number of factors with probability approaching one. Both the LASSO estimator and the conservative LASSO estimator are employed to improve estimation precision. The conservative LASSO estimates of the non-zero coefficients are shown to be asymptotically equivalent to the oracle least squares estimates. Simulations demonstrate that our estimators perform reasonably well in finite samples given the complex high dimensional nature of the model with multiple unobserved components. In an empirical illustration we apply the methodology to explore the dynamic connectedness in the volatilities of financial asset prices and the transmission of investor fear. The findings reveal that a large proportion of connectedness is due to common factors. Conditional on the presence of these common factors, the results still document remarkable connectedness due to the interactions between the individual variables, thereby supporting a common factor augmented VAR specification.

Keywords: Common factors; Connectedness; Cross-sectional dependence; Investor fear; High-dimensional VAR; Nuclear-norm regularization (search for similar items in EconPapers)
JEL-codes: C13 C33 C38 C51 (search for similar items in EconPapers)
Pages: 70 pages
Date: 2020-08
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Journal Article: High-dimensional VARs with common factors (2023)
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