  This paper introduces a new stochastic process with values in the set Z of
integers with sign. The increments of process are Poisson differences and the
dynamics has an autoregressive structure. We study the properties of the
process and exploit the thinning representation to derive stationarity
conditions and the stationary distribution of the process. We provide a
Bayesian inference method and an efficient posterior approximation procedure
based on Monte Carlo. Numerical illustrations on both simulated and real data
show the effectiveness of the proposed inference.
