The College of Administration and Economics at the University of Baghdad discussed, a PhD dissertation in field of Statistics by the student (Rand Haitham Abdul Hussein ) and tagged with (Conditional prediction from INAR(P) model with application ) , Under supervision of (Prof. Dr. Suhail Najm Abdullah )
Many studies and research have shown the efficiency and flexibility of Box-Jenkins (ARMA) models in estimating and forecasting time series. However, these models suffer from some limitations when predicting events that take non-negative integer values such as the number of patients or the number of traffic accidents. Therefore, the INAR model for non-negative integers was used, which is based on a binomial thinning operator that produces integers. Time series analysis is an important statistical tool for understanding future patterns and helps in understanding future plans.
The INAR model was used in this thesis to predict the number of cattle infected with foot-and-mouth disease, due to the importance of achieving accurate predictions in order to reduce losses resulting from the spread of the disease and control it effectively. The thesis aimed to improve the predictions using the INAR model, whether through individual models or improved models. The INAR model was estimated using three methods: conditional least squares (CLS) estimation, Yule-Walker (YW) method, and conditional maximum likelihood (CML) method. Two probability distributions were adopted: Poisson and geometric in the experimental aspect. In addition, two thinning operators, the binomial thinning operator, and the negative binomial thinning operator were used to obtain accurate predictions using these methods. To improve the accuracy of the predictions, the support vector regression algorithm (SVR) was applied as one of the performance improvement methods. The parameters of the SVR algorithm were also improved using the genetic algorithm (GA) and the particle swarm algorithm (PSO).
The simulation results showed that the proposed methods perform better in prediction than the conventional methods conducted on the time series using the INAR model for different sample sizes and different values of the lambda parameter. When the model was applied to raw data on the number of cattle infected with FMD during the period from December 2016 to January 2023, the results showed that the improved models were more efficient in prediction compared to the single model.
The performance of the models was compared using two metrics, the mean squared error (MSE) and the mean absolute error (MAE), with the improved models proving superior in prediction accuracy, making them the most suitable for application in this field.
