Journal of the Iranian Statistical Society

Poisson-Lindley INAR(1) Processes: Some Estimation and Forecasting Methods

Authors

1 department of statistics, Faculty of science, Fasa University

2 department of statistics, Faculty of science, Shiraz University

10.52547/jirss.19.2.145

Abstract

This paper focuses on different methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predicted value for h-step ahead of the series is obtained. Some simulations and a real data analysis are applied to compare the presented estimations and the prediction methods.

Keywords

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On the application of integer-valued time series models for the analysis of disease incidence. Statistics in Medicine, 18(15), 2025-2039. Chuang, C. S., & Chan, N. H. (2002). Empirical likelihood for autoregressive models, with applications to unstable time series. Statistica Sinica, 387-407. Fokianos, K., & Kedem, B. (2003). Regression theory for categorical time series. Statistical science, 18(3), 357-376. Fox, R., & Taqqu, M. S. (1986). Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The Annals of Statistics, 517-532. Freeland, R. K., & McCabe, B. P. (2004). Forecasting discrete valued low count time series. International Journal of Forecasting, 20(3), 427-434. Ghitany, M. E., & Al-Mutairi, D. K. (2009). Estimation methods for the discrete Poisson-Lindley distribution. Journal of Statistical Computation and Simulation, 79(1), 1-9. Hannan, E. J. (1973). The asymptotic theory of linear time-series models. 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Journal of the Iranian Statistical Society
Volume 19, Issue 2
December 2020
Pages 145-173
  • Receive Date: 23 July 2022
  • Revise Date: 10 May 2024
  • Accept Date: 23 July 2022