References
- Al-Osh, M. A., and A. A. Alzaid. 1987. First order integer-valued autoregressive (INAR(1)) processes. Journal of Time Series Analysis 8 (3):261–75. doi:10.1111/j.1467-9892.1987.tb00438.x.
- Awale, M., T. V. Ramanathan, and M. Kale. 2021. Coherent forecasting in integer-valued AR(1) models with geometric marginals. Journal of Data Science 15 (1):95–114. doi:10.6339/JDS.201701_15(1).0006.
- Boucher, J. P., M. Denuit, and M. Guillén. 2008. Model of insurance claim counts with time dependence based on generalization of Poisson and negative binomial distributions. Variance 2 (1):135–62.
- Chen, C. W. S., M. K. P. So, J. C. Li, and S. Sriboonchitta. 2016. Autoregressive conditional negative binomial model applied to over-dispersed time series of counts. Statistical Methodology 31:73–90. doi:10.1016/j.stamet.2016.02.001.
- Czado, C.,. T. Gneiting, and L. Held. 2009. Predictive model assessment for count data. Biometrics 65 (4):1254–61. doi:10.1111/j.1541-0420.2009.01191.x.
- Freeland, R. K., and B. P. M. McCabe. 2004. Forecasting discrete low count time series. International Journal of Forecasting 20 (3):427–34. doi:10.1016/S0169-2070(03)00014-1.
- Gneiting, T. 2011. Making and evaluating point forecasts. Journal of the American Statistical Association 106 (494):746–62. doi:10.1198/jasa.2011.r10138.
- Gneiting, T., F. Balabdaoui, and A. E. Raftery. 2007. Probabilistic forecasts, calibration and sharpness. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 69 (2):243–368. doi:10.1111/j.1467-9868.2007.00587.x.
- Held, L., and M. Paul. 2012. Modelling seasonality in space-time infectious disease surveillance data. Biometrical Journal 54 (6):824–43. doi:10.1002/bimj.201200037.
- Homburg, A., C. H. Weiß, L. C. Alwan, G. Frahm, and R. Göb. 2019. Evaluating approximate point forecasting of count processes. Econometrics 7 (3):30. doi:10.3390/econometrics7030030.
- Jung, R. C., and A. R. Tremayne. 2006. Coherent forecasting in integer time series models. International Journal of Forecasting 22 (2):223–38. doi:10.1016/j.ijforecast.2005.07.001.
- Jung, R. C., and A. R. Tremayne. 2011. Convolution-closed models for count time series with applications. Journal of Time Series Analysis 32 (3):268–80. doi:10.1111/j.1467-9892.2010.00697.x.
- Kashikar, A. S., N. Rohan, and T. V. Ramanathan. 2013. Integer autoregressive models with structural breaks. Journal of Applied Statistics 40 (12):2653–69. doi:10.1080/02664763.2013.823920.
- Kim, H.-Y., and Y. Park. 2010. Coherent forecasting in binomial AR(p) model. Communications of the Korean Statistical Society 17 (1):27–37.
- Livio, T., N. Mamode Khan, M. Bourguignon, and H. S. Bakouch. 2018. An INAR(1) model with Poisson-Lindley innovations. Economics Bulletin 38 (3):1505–13.
- Maiti, R., and A. Biswas. 2015a. Coherent forecasting for over-dispersed time series of counts data. Brazilian Journal of Probability and Statistics 29 (4):747–66. doi:10.1214/14-BJPS244.
- Maiti, R., and A. Biswas. 2015b. Coherent forecasting for stationary time series of discrete data. AStA Advances in Statistical Analysis 99 (3):337–65. doi:10.1007/s10182-014-0243-3.
- McKenzie, E. 1986. Autoregressive moving-average processes with negative-binomial and geometric marginal distributions. Advances in Applied Probability 18 (3):679–705. doi:10.2307/1427183.
- Mohammadpour, M., H. S. Bakouch, and M. Shirozhan. 2018. Poisson-Lindley INAR(1) model with applications. Brazilian Journal of Probability and Statistics 32 (2):262–80. doi:10.1214/16-BJPS341.
- Ristić, M. M., A. S. Nastić, and H. S. Bakouch. 2012. Estimation in an integer-valued autoregressive process with negative binomial marginals (NBINAR(1)). Communications in Statistics - Theory and Methods 41 (4):606–18. doi:10.1080/03610926.2010.529528.
- Ristić, M. M., H. S. Bakouch, and A. S. Nastić. 2009. A new geometric first order integer-valued autoregressive (NGINAR(1)) process. Journal of Statistical Planning and Inference 139 (7):2218–26. doi:10.1016/j.jspi.2008.10.007.
- Steutel, F. W., and K. Van Harn. 1979. Discrete analogues of self-decomposability and stability. Annals of Probability 7:893–99.
- Wang, Y., and H. Zhang, 2021. Some estimation and forecasting procedures in Poisson- Lindley INAR(1) process. Communications in Statistics-Simulation and Computation 50 (1):49–62. doi:10.1080/03610918.2018.1547402.
- Weiß, C. H., and M. H.-J M. Feld. 2019. On the performance of information criteria for model identification of count time series. Studies in Nonlinear Dynamics and Econometrics 24 (1):1–16. doi:10.1515/snde-2018-0012.