Causal Vector Autoregression Enhanced with Covariance and Order Selection

Bolla, Marianna; Ye, Dongze; Wang, Haoyu; Ma, Renyuan; Frappier, Valentin; Thompson, William; Donner, Catherine; Baranyi, Máté; Abdelkhalek, Fatma

doi:10.6082/apvbv-7s794

Published February 24, 2023 | Version v1

Journal article Open

Causal Vector Autoregression Enhanced with Covariance and Order Selection

1. Budapest University of Technology and Economics
2. University of Southern California
3. University of Chicago
4. Yale University
5. Nantes University
6. University of Cincinnati
7. University of Oklahoma
8. Assiut University

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.

Data availability

The third-party financial dataset analyzed in the current study is available in the UCI Machine Learning Repository, and was collected by the authors of Akbilgic et al. (2014). The dataset is available in: Dua, D. and Graff, C. (219). UCI Machine Learning Repository, Irvine, CA: University of California, School of Information and Computer Science, https://archive.ics.uci.edu/ml/datasets/ISTANBUL+STOCK+EXCHANGE (accessed on 1 August 2022). The World Bank Data on infant mortality rates are available on https://data.worldbank.org/indicator (accessed on 1 August 2022); see also Abdelkhalek and Bolla (2020).

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