  Integer-valued time series models have been a recurrent theme considered in
many papers in the last three decades, but only a few of them have dealt with
models on $\mathbb Z$ (that is, including both negative and positive integers).
Our aim in this paper is to introduce a first-order integer-valued
autoregressive process on $\mathbb Z$ with skew discrete Laplace marginals
(Kozubowski and Inusah, 2006). For this, we define a new operator that acts on
two independent latent processes, similarly as made by Freeland (2010). We
derive some joint and conditional basic properties of the proposed process such
as characteristic function, moments, higher-order moments and jumps. Estimators
for the parameters of our model are proposed and their asymptotic normality are
established. We run a Monte Carlo simulation to evaluate the finite-sample
performance of these estimators. In order to illustrate the potentiality of our
process, we apply it to a real data set about population increase rates.
