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High-Dimensional VARs with Common Factors

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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.

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  • Ke Miao & Peter C.B. Phillips & Liangjun Su, 2020. "High-Dimensional VARs with Common Factors," Cowles Foundation Discussion Papers 2252, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2252
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    Cited by:

    1. Christian Brownlees & Gu{dh}mundur Stef'an Gu{dh}mundsson, 2021. "Performance of Empirical Risk Minimization for Linear Regression with Dependent Data," Papers 2104.12127, arXiv.org, revised May 2023.
    2. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Inference in Non-stationary High-Dimensional VARs," Papers 2302.01434, arXiv.org, revised Sep 2023.
    3. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    4. Wang, Yiren & Phillips, Peter C.B. & Su, Liangjun, 2024. "Panel data models with time-varying latent group structures," Journal of Econometrics, Elsevier, vol. 240(1).
    5. Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).

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    More about this item

    Keywords

    Common factors; Connectedness; Cross-sectional dependence; Investor fear; High-dimensional VAR; Nuclear-norm regularization;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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