Composite likelihood expectation-maximization algorithm for the first-order multivariate integer-valued autoregressive model with multivariate mixture distributions

doi:10.1016/j.matcom.2025.04.017

Composite likelihood expectation-maximization algorithm for the first-order multivariate integer-valued autoregressive model with multivariate mixture distributions

2025-06-05

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DOI：10.1016/j.matcom.2025.04.017

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In this paper, we develops a estimation framework for first-order multivariate integer-valued autoregressive (MINAR(1)) models with multivariate Poisson-lognormal (MPL) or multivariate geometric-logitnormal (MGL) innovations. Owing to the structural complexity of the MINAR(1) framework and the latent dependence in MPL/MGL innovation processes, the likelihood functions involve summations and integrals. Traditional expectation-maximization (EM) algorithms face prohibitive computational demands as model dimensionality increases. To address this, we propose a composite likelihood expectation-maximization (CLEM) algorithm that strategically combines composite likelihood with the EM algorithm, reducing the computational burden. Furthermore, we implement a Cholesky parameterization for the covariance matrix to ensure positive definiteness. Through comprehensive Monte Carlo simulations, we demonstrate the performance of CLEM algorithm. Finally, we validate the method's practical utility by analyzing a real-world dataset.

Keywords:

Integer-valued time series

Thinning operator

Composite likelihood EM algorithm

Multivariate Poisson-lognormal distribution

Multivariate geometric-logitnormal distribution

Composite likelihood expectation-maximization algorithm for the first-order multivariate integer-valued autoregressive model with multivariate mixture distributions

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