True Integer Valued Autoregressive Model with Skellam Distribution

Authors

M. M. Gabr, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, EgyptFollow
M. A. Darwish, Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, EgyptFollow
H. A. Hashem, Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, EgyptFollow
L. M. Fatehy, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In the present article, we introduce a new true integer valued autoregressive model of order one TPDINAR(1) for data sets on Z and either positive or negative correlations based on the Poisson difference (Skellam) marginal distribution and using a random walk variable (It). Properties of the model are derived. We consider several methods for estimating the unknown parameters of the model, and their properties are discussed. Simulations are carried out for the performance of these estimators for illustrative purposes. Finally, the analysis of real life time series data is presented, and its performance is compared to two different INAR(1) models that may also be used over the observed data.

Digital Object Identifier (DOI)

https://dx.doi.org/10.18576/jsap/130130

Recommended Citation

M. Gabr, M.; A. Darwish, M.; A. Hashem, H.; and M. Fatehy, L. (2024) "True Integer Valued Autoregressive Model with Skellam Distribution," Journal of Statistics Applications & Probability: Vol. 13: Iss. 1, Article 30.
DOI: https://dx.doi.org/10.18576/jsap/130130
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol13/iss1/30