Re-visiting the COVID-19 analysis using the class of high ordered integer-valued time series models with harmonic features

Naushad Mamode Khan; Ashwinee Devi Soobhug; Noha Youssef; Swalay Fedally; Saralees Nadarajah; Zaid Heetun

doi:10.1016/j.health.2022.100086

Re-visiting the COVID-19 analysis using the class of high ordered integer-valued time series models with harmonic features

Healthc Anal (N Y). 2022 Nov:2:100086. doi: 10.1016/j.health.2022.100086. Epub 2022 Aug 9.

Authors

Naushad Mamode Khan¹, Ashwinee Devi Soobhug², Noha Youssef³, Swalay Fedally⁴, Saralees Nadarajah⁵, Zaid Heetun⁴

Affiliations

¹ Faculty of Social Sciences and Humanities, University of Mauritius, Réduit, Mauritius.
² Statistics Mauritius, Ministry of Finance, Economic Planning and Development, Port-Louis, Mauritius.
³ American University of Egypt, Cairo, Egypt.
⁴ Ministry of Health and Wellness, Port-Louis, Mauritius.
⁵ Department of Mathematics, University of Manchester, Manchester, United Kingdom.

Abstract

The COVID-19 series is obviously one of the most volatile time series with lots of spikes and oscillations. The conventional integer-valued auto-regressive time series models (INAR) may be limited to account for such features in COVID-19 series such as severe over-dispersion, excess of zeros, periodicity, harmonic shapes and oscillations. This paper proposes alternative formulations of the classical INAR process by considering the class of high-ordered INAR models with harmonic innovation distributions. Interestingly, the paper further explores the bivariate extension of these high-ordered INARs. South Africa and Mauritius' COVID-19 series are re-scrutinized under the optic of these new INAR processes. Some simulation experiments are also executed to validate the new models and their estimation procedures.

Keywords: COVID-19 deaths; Estimation; Harmonic innovations; INAR( $p$ ); Simulation.