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

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