Maximum-likelihood estimation of the Po-MDDRCINAR(p) model with analysis of a COVID-19 data

Xiufang Liu, Jianlong Peng, Dehui Wang and Huaping Chen

Statistical Theory and Related Fields, 2025, vol. 9, issue 1, 34-58

Abstract: Integer-valued data are frequently encountered in time series studies. A pth-order mixed dependence-driven random coefficient integer-valued autoregressive time series model (Po-MDDRCINAR(p)) in view of binomial and negative binomial operators, where the innovation sequence follows a Poisson distribution, is investigated to provide meaningful theoretical explanations. Strict stationary and ergodicity of the model are demonstrated. Furthermore, the conditional least-squares and conditional maximum-likelihood methods are adopted to estimate the parameters, where the asymptotic characterization of the estimators is derived. Finite-sample properties of the conditional maximum-likelihood estimator are examined in relation to the widely used conditional least-squares estimator. The conclusion is that, if the Poisson assumption of the innovation sequence can be justified, conditional maximum-likelihood method performs better in terms of MADE and MSE. Finally, the practical performance of the model is illustrated by a set of COVID-19 data of suspected cases in China with a comparison with relevant models that exist so far in the literature.

Date: 2025
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DOI: 10.1080/24754269.2024.2412491

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