Introduction

Time series of counts are encountered in almost every discipline of research, ranging from the epidemiological [ Cardinal et al., 1999 , Yu et al., 2013 ], environmental [ Cui and Lund, 2009 , Scotto et al., 2014b ], meteorological [ Tukey, 1949 ], bio-pharmaceutical [ Al Osh, 2009 ], economics and financial [ Blundell et al., 1999 , Brännäs and Hellström, 2001 , Quoreshi, 2006 ], and transport [ Karlis and Xekalaki, 2005 , Sunechar et al., 2018b , Jowaheer et al., 2019 , Mamode Khan et al., 2021 ] to other interdisciplinary studies [ Weiß, 2018 , Brannas and Quoreshi, 2010 , Bourgignon et al., 2018 , Bareto Souza, 2015 , Lambert, 1992 , Hellström, 2001 ].