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Inference for INAR$\left(p\right)$ processes with signed generalized power series thinning operator. (English) Zbl 1177.62110
Summary: We propose a $p$ th-order integer-valued autoregressive processes with a signed generalized power series thinning operator. Strict stationarity, ergodicity of the process, and the moments and autocovariance functions are obtained. We derive Yule-Walker and conditional least squares estimators for the parameters in the model and their asymptotic properties are established. The performances of these estimators are compared via simulations, and we also study the robustness of these estimates. At last, the model is applied to a real data set.
MSC:
 62M10 Time series, auto-correlation, regression, etc. (statistics) 62F12 Asymptotic properties of parametric estimators 62H12 Multivariate estimation 65C60 Computational problems in statistics 15A16 Matrix exponential and similar functions of matrices