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

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 rege...

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Bibliographic Details
Published inStatistics (Berlin, DDR) Vol. 58; no. 2; pp. 336 - 363
Main Authors Bertail, Patrice, Garay, Aldo M., Medina, Francyelle L., Jales, Isaac C.S.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.03.2024
Taylor & Francis Ltd
Subjects
Algorithms
Asymptotic methods
Autoregressive processes
Bootstrap method
Confidence intervals
Count time series
EM algorithm
Estimation
Forecasting
Innovations
Maximum likelihood method
Parameters
regenerative bootstrap
Simulation
Statistical analysis
Statistical methods
Time series
zero-inflated distribution
ZI-INAR(p) process
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Summary: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.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331888.2024.2344670