A p-Order signed integer-valued autoregressive (SINAR(p)) model

In this article, we propose an extension of integer-valued autoregressive INAR models. Using a signed version of the thinning operator, we define a larger class of -valued processes, called SINAR, which can have positive as well as negative correlations. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. In particular, it is shown that the autocorrelation function of any real-valued AR process can be recovered with a SINAR process, which improves INAR modeling.