Causal Vector Autoregression Enhanced with Covariance and Order Selection

TL;DR

This paper introduces a causal vector autoregressive model that combines graphical models and covariance selection to analyze multivariate processes, with applications to real data and order selection techniques.

Contribution

It proposes a novel CVAR model integrating DAG-based structure and covariance selection, improving modeling of multivariate time series.

Findings

Effective estimation of path coefficients using block Cholesky decomposition.

Application of covariance selection to enforce zero constraints in the model.

Use of information criteria for optimal order selection in real data applications.

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 $p\ge 1$ of the fitted CVAR$(p)$ model, order selection is performed with various information criteria.