Causal Vector Autoregression Enhanced with Covariance and Order Selection

Marianna Bolla (), Dongze Ye, Haoyu Wang, Renyuan Ma, Valentin Frappier, William Thompson, Catherine Donner, Máté Baranyi and Fatma Abdelkhalek
Additional contact information
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

Econometrics, 2023, vol. 11, issue 1, 1-30

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.

Keywords: structural vector autoregression; causality along a DAG; block Cholesky decomposition; covariance selection; order selection (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2023
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