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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 $$ X_t=\sum_{i=1}^p\varphi_i^{(t)}\circ X_{t-i}+Z_i, $$ where $X_t$ is the observed time series, $\varphi_i^{(t)}$ is an i.i.d. sequence on [0,1] with $\text{\bf E}\varphi_i^{(t)}=\varphi_i$, $Z_i$ are i.i.d. non-negative integer-valued, with $\text{\bf E}Z_i=\lambda$, 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 $\varphi_i$ and $\lambda$) are discussed. Their asymptotic distributions are investigated. Results of simulations and applications to medical data are presented.
Reviewer: R. E. Maiboroda (Kyïv)

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