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Keywords:

  • INAR(p) models;
  • Binomial thinning;
  • Negative binomial thinning;
  • Geometric marginal distribution

A mixed integer-valued autoregressive model of order p is proposed. The existence of this unique, stationary and ergodic process is proved and its autocorrelation structure and some conditional stochastic characteristics are derived. Model parameters are estimated via Yule-Walker, conditional least squares and conditional maximum likelihood methods. Finally, possible application of the model to real data sets is considered.