A maximum likelihood and regenerative bootstrap approach for estimation and forecasting of INAR(p) processes with zero-inflated innovations

Abstract

In this work, we study a class of p-order non-negative integer-valued autoregressive (INAR(p)) processes, with innovations following zero-inflated (ZI) distributions called ZI-INAR(p) processes. Based on the EM algorithm, we present an estimation procedure of parameters model. We also develop a regenerative bootstrap method to construct confidence intervals for the parameters as well as to estimate the forecasting distributions for future values. We discuss asymptotic properties of the regenerative bootstrap method. The performance of the proposed methods is evaluated considering the analysis of two simulation studies and a real dataset.

Keywords:

• Count time series
• ZI-INAR(p) process
• regenerative bootstrap
• EM algorithm
• zero-inflated distribution

Acknowledgements

The authors thank the editor, associate editor and anonymous reviewers whose constructive criticism led to improved presentation and quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Aldo M. Garay would like to acknowledge the support of the Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco (FACEPE – Grant APQ-0950-1.02/22) and by Grant 441476/2023-6 from National Council for Scientific and Technological Development – CNPq – Brazil. This study was also conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01).