Modeling Time Series Poison Count Data: An Application to COVID 19 Confirmed Cases in Nigeria

1Bashir Alhaji Mustapha, 2Harun R. Bakari and 2Yusuf A. Mohammed

1Department of Statistics, Federal Polytechnic Damaturu, Nigeria
2Department of Mathematical Sciences, University of Maiduguri, Nigeria

*Corresponding author:,


Time series events are counted within time intervals usually for convenience and practical reasons. Time series data involving counts frequently follows Poison distribution. Integrated Autoregressive Moving Average (ARIMA) models were studied on simulated Poison data of different parameter and sample sizes. These models were used to capture Poison data with different phenomena. Data set were simulated from Poison process with ARIMA (p, d, q) were then fitted to the simulated data so as to examine the effect of the changes in parameter value of the Poison on the models’ performance across the sample size. Thereafter, the same models were used to fit and forecast the daily Covid-19 data, confirmed cases from inception to February 2023. It was concluded that ARIMA (2, 1, 2) and ARIMA (1, 1, 1) are obviously the best Models at different sample sizes respectively. Based on the Covid-19 analysis, the estimated coefficient values of all ARIMA (p,d,q) strictly conforms to the bounds of the parameter between -1 and 1 and this had made the model to be stationary comparing the ARIMA models in terms of the AIC, BIC and MSE. It is clearly preferred ARIMA (1, 0, 2) to other models since their estimated AIC, BIC and MSE are smaller as compared to other models. The forecast is quite accurate, and hereby confirms what was expected. It seems that ARIMA (1, 0, 2) does a very good job in capturing the dynamic nature of the data and forecasting. It was observed that the confirmed cases increase, and then keep stationary throughout the future times.


COVID-19 data,
Poison data,