A mixed INAR(p) model with serially dependent innovation with application to some COVID-19 data

Abstract.

This present work proposes a new mixed INAR(p) model (SDMINAR(p)) based on binomial thinning and negative binomial thinning operators, where the innovations are supposed to be serially dependent on the population at time $\{t-1,t-2,\cdots ,t-p\}$. Stationarity and ergodicity properties are given. Conditional least squares and weighted conditional least squares are adopted to estimate the model parameters. The asymptotic normality property of the estimators is presented. The performances of these estimators are investigated and compared by simulation, which manifests that the weight conditional least squares perform better than the conditional least squares. Finally, the COVID-19 data of severe cases in China and severe cases imported from outside China are analyzed to demonstrate the practical relevance of the model.

Keywords:

• SDMIANR(p) model
• conditional least squares
• weighted conditional least squares
• asymptotic normality
• COVID-19 data

Disclosure statement

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

Acknowledgments

Thank you all for helping me writing this LaTeX sample file.

Additional information

Funding

This work is supported by Fundamental Research Program of Shanxi Province (Grant No.202103021223084) and Natural Science Foundation of Henan Province(No.222300420127).