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Inference for p th-order random coefficient integer-valued autoregressive processes. (English) Zbl 1126.62086

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

X t = i=1 p φ i (t) X t-i +Z i ,

where X t is the observed time series, φ i (t) is an i.i.d. sequence on [0,1] with Eφ i (t) =φ i , Z i are i.i.d. non-negative integer-valued, with EZ i =λ, and 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 φ i and λ) are discussed. Their asymptotic distributions are investigated. Results of simulations and applications to medical data are presented.

MSC:
62M10Time series, auto-correlation, regression, etc. (statistics)
62M09Non-Markovian processes: estimation
62E20Asymptotic distribution theory in statistics
62P10Applications of statistics to biology and medical sciences