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Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach

Author

Listed:
  • Vladica S. Stojanović

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11060 Belgrade, Serbia)

  • Hassan S. Bakouch

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
    Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt)

  • Eugen Ljajko

    (Department of Mathematics, Faculty of Sciences & Mathematics, University of Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia)

  • Najla Qarmalah

    (Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia)

Abstract

Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probability-generating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.

Suggested Citation

  • Vladica S. Stojanović & Hassan S. Bakouch & Eugen Ljajko & Najla Qarmalah, 2023. "Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1772-:d:1118434
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    References listed on IDEAS

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