A th-order random coefficient integer-valued autoregressive (RCINAR(p)) model is considered of the form
where is the observed time series, is an i.i.d. sequence on [0,1] with , are i.i.d. non-negative integer-valued, with , and is the thinning operator. Existence of stationary solutions is demonstrated for this model. Conditional and unconditional mean and variance of are derived. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized moment estimators for the parameters of the model (especially for and ) are discussed. Their asymptotic distributions are investigated. Results of simulations and applications to medical data are presented.