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Zero truncated Poisson integer-valued AR\((1)\) model. (English) Zbl 1200.62099

Summary: We introduce a new stationary integer-valued autoregressive process of first order with zero truncated Poisson marginal distributions. We consider some properties of this process, such as autocorrelations, spectral density and multi-step ahead conditional expectation, variance and probability generating function. Stationary solutions and their uniqueness are obtained with a discussion of strict stationarity and ergodicity of such processes. We estimate the unknown parameters by using conditional least squares estimation, nonparametric estimation and maximum likelihood estimation. The asymptotic properties and asymptotic distributions of the conditional least squares estimators have been investigated. Some numerical results of the estimators are presented and some sample paths of the process are illustrated. Some possible applications of the introduced model are discussed.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

Software:

BRENT; R
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References:

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