INAR(1) process with weighted negative binomial Lindley distributed innovations and applications to criminal and COVID-19 data

Abstract

In this study, we introduce a pliant stationary first-order integer-valued autoregressive (INAR) process with weighted negative binomial Lindley innovations. The main properties of the model are derived. The methods of conditional maximum likelihood, conditional least square and Yule-Walker are used for estimating the process parameters, while the efficiency of these three methods is evaluated through a simulation study. Finally, the practical aspect of the proposed INAR(1) process is discussed on two time series of the monthly number of criminal mischief reports in Pittsburgh and the daily COVID-19 death cases in Paraguay.

Keywords:

• Binomial thinning operator
• Count data
• Dispersion
• Estimation
• Simulation MSC: 62M10

Disclosure statement

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

Notes

1 Equation (4)(4) $$\begin{array}{c}F{I}_{ϵ}=\frac{{\sigma }_{ϵ}^2}{{\mu }_{ϵ}}=\frac{1}{1-p}\hspace{0.17em}+\hspace{0.17em}\frac{1}{1+p({\beta }^2-1)}\hspace{0.17em}-\hspace{0.17em}\frac{1+\beta }{1+\beta +p({\beta }^2-1)}.\hfill \end{array}$$(4) is the corrected expression of ID from Bakouch (2018), page 2623.