A new class of Z-valued INAR(1) models with application to mutual fund flows

$Z$-valued time series, which have discrete and quantitative observations on the set $Z=\{...,-2,-1,0,1,2,\dots \}$, are commonly observed in economics and finance. $Z$-valued versions of integer-valued autoregressive (INAR) models are frequently employed to fit $Z$-valued time series. However, the existing $Z$-valued INAR models encounter difficulties in data generation mechanism and statistical inference. To enhance the modeling and prediction of $Z$-valued time series, this article constructs a class of $Z$-valued INAR(1) models from a new perspective and studies the related statistical inference problem. Empirically, an application to mutual fund flows demonstrates that our model offers satisfactory performance in economics and finance.