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Causal Vector Autoregression Enhanced with Covariance and Order Selection

Author

Listed:
  • Marianna Bolla

    (Department of Stochastics, Budapest University of Technology and Economics, 1111 Budapest, Hungary)

  • Dongze Ye

    (Department of Computer Science, University of Southern California, Los Angeles, CA 90007, USA)

  • Haoyu Wang

    (Committee on Computational and Applied Mathematics, University of Chicago, Chicago, IL 60637, USA)

  • Renyuan Ma

    (Department of Statistics, Yale University, New Haven, CT 06520, USA)

  • Valentin Frappier

    (UFR Sciences and Techniques, Nantes University, 44035 Nantes, France)

  • William Thompson

    (Lindner College of Business, University of Cincinnati, Cincinnati, OH 45221, USA)

  • Catherine Donner

    (Data Science and Analytics Institute, University of Oklahoma, Norman, OK 73019, USA)

  • Máté Baranyi

    (Department of Stochastics, Budapest University of Technology and Economics, 1111 Budapest, Hungary)

  • Fatma Abdelkhalek

    (Department of Statistics, Mathematics, and Insurance, Faculty of Commerce, Assiut University, Assiut Governorate 71515, Egypt)

Abstract

A causal vector autoregressive (CVAR) model is introduced for weakly stationary multivariate processes, combining a recursive directed graphical model for the contemporaneous components and a vector autoregressive model longitudinally. Block Cholesky decomposition with varying block sizes is used to solve the model equations and estimate the path coefficients along a directed acyclic graph (DAG). If the DAG is decomposable, i.e., the zeros form a reducible zero pattern (RZP) in its adjacency matrix, then covariance selection is applied that assigns zeros to the corresponding path coefficients. Real-life applications are also considered, where for the optimal order p ≥ 1 of the fitted CVAR ( p ) model, order selection is performed with various information criteria.

Suggested Citation

  • Marianna Bolla & Dongze Ye & Haoyu Wang & Renyuan Ma & Valentin Frappier & William Thompson & Catherine Donner & Máté Baranyi & Fatma Abdelkhalek, 2023. "Causal Vector Autoregression Enhanced with Covariance and Order Selection," Econometrics, MDPI, vol. 11(1), pages 1-30, February.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:1:p:7-:d:1079607
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    References listed on IDEAS

    as
    1. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, August.
    2. Brillinger, David R., 1996. "Remarks Concerning Graphical Models for Time Series and Point Processes," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 16(1), November.
    3. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.
    4. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    5. Keating, John W., 1996. "Structural information in recursive VAR orderings," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1557-1580.
    Full references (including those not matched with items on IDEAS)

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