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The main subject of this paper is a combined integer-valued autoregressive time series with both positive and negative values, based on a new thinning operator. Some important properties are analyzed. Estimators of the unknown parameters are derived and their asymptotic behavior is analyzed. A simulation and an application on real-data are also shown. In the end, a mechanism for identification and prediction of the latent dimensions of the model are presented.

A COMBINED SDLINAR(p) MODEL AND IDENTIFICATION AND PREDICTION OF ITS LATENT COMPONENTS