*(English)*Zbl 1126.62086

A $p$ th-order random coefficient integer-valued autoregressive (RCINAR(p)) model is considered of the form

where ${X}_{t}$ is the observed time series, ${\phi}_{i}^{\left(t\right)}$ is an i.i.d. sequence on [0,1] with $\mathbf{\text{E}}{\phi}_{i}^{\left(t\right)}={\phi}_{i}$, ${Z}_{i}$ are i.i.d. non-negative integer-valued, with $\mathbf{\text{E}}{Z}_{i}=\lambda $, and $\circ $ is the thinning operator. Existence of stationary solutions is demonstrated for this model. Conditional and unconditional mean and variance of ${X}_{t}$ are derived. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized moment estimators for the parameters of the model (especially for ${\phi}_{i}$ and $\lambda $) are discussed. Their asymptotic distributions are investigated. Results of simulations and applications to medical data are presented.

##### MSC:

62M10 | Time series, auto-correlation, regression, etc. (statistics) |

62M09 | Non-Markovian processes: estimation |

62E20 | Asymptotic distribution theory in statistics |

62P10 | Applications of statistics to biology and medical sciences |