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


Correspondence to: Lionel Truquet, UMR 6625 CNRS Institut de Recherche Mathématique de Rennes (IRMAR) Université de Rennes I, Campus de Beaulieu, F-35042 Rennes Cedex, France.


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 inline image-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.