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Keywords:

  • Integer-valued time series;
  • autoregressive model;
  • signed thinning operator
  • Primary: 62M10;
  • Secondary: 62M20

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.