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Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix

Author

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  • Benjamin Poignard

    (Graduate School of Economics, Osaka University)

  • Manabu Asai

    (Faculty of Economics, Soka University)

Abstract

We consider the problem of estimating sparse structural vector autoregression (SVAR) processes via penalized precision matrix. Such matrix is the output of the underlying directed acyclic graph of the SVAR process, whose zero components correspond to zero SVAR coecients. The precision matrix estimators are deduced from the class of Bregman divergences and regularized by the SCAD, MCP and LASSO penalties. Under suitable regularity conditions, we derive error bounds for the regularized precision matrix for each Bregman divergence. Moreover, we establish the support recovery property, including the case when the penalty is non-convex. These theoretical results are supported by empirical studies.

Suggested Citation

  • Benjamin Poignard & Manabu Asai, 2021. "Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix," Discussion Papers in Economics and Business 21-03, Osaka University, Graduate School of Economics.
    • Handle: RePEc:osk:wpaper:2103
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    References listed on IDEAS

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    1. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    2. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June.
    3. Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
    4. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    5. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    6. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    8. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
    9. Dedecker, Jérôme & Fan, Xiequan, 2015. "Deviation inequalities for separately Lipschitz functionals of iterated random functions," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 60-90.
    10. Adam J. Rothman & Elizaveta Levina & Ji Zhu, 2010. "A new approach to Cholesky-based covariance regularization in high dimensions," Biometrika, Biometrika Trust, vol. 97(3), pages 539-550.
    11. Wei Biao Wu, 2003. "Nonparametric estimation of large covariance matrices of longitudinal data," Biometrika, Biometrika Trust, vol. 90(4), pages 831-844, December.
    12. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    13. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, vol. 99(1), pages 39-61, November.
    14. Teng Zhang & Hui Zou, 2014. "Sparse precision matrix estimation via lasso penalized D-trace loss," Biometrika, Biometrika Trust, vol. 101(1), pages 103-120.
    15. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    16. Oxley, Les & Reale, Marco & Wilson, Granville Tunnicliffe, 2009. "Constructing structural VAR models with conditional independence graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2910-2916.
    17. Granville Tunnicliffe Wilson & Marco Reale, 2008. "The sampling properties of conditional independence graphs for I(1) structural VAR models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 802-810, September.
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    Cited by:

    1. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.

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    Keywords

    sparse structural vector autoregression; statistical consistency; support recovery.;
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