Forecasting Non-Gaussian Time Series with TB Data - Lamyaa Mohammed Ali Hameed (International Journal of Computational and Experimental Science and Engineering, 2025)
Abstract Conventional forecasting models require time series that are stationary over time in terms of mean and variance. However, we often encounter data that rarely meet this condition. The data may have Non- Gaussian (N-G) distribution or contain heavy tails or extreme values. In order to improve and strengthen the predictive performance, various (N-G) models have been used, each of which has a different property from the other models. The combined formulas of discrete distributions such as Poisson or Negative – Binomial (NB) distribution with Autoregressive Integrated Moving Average (ARIMA) models provide an interpretable methodology when modeling time series data by following the characteristics of count data because it relies on the distributional properties represented by the general linear model based on count data and the time dependence represented by the ARIMA model of the residuals. Predicting time- dependent patterns of count data involves complexities resulting from the discrete and positive nature of the data, which is not compatible with the classical ARIMA methodology. To address this shortcoming, models combining the two were used as an alternative solution. These models are Gamma-ARIMA, Poisson-ARIMA, and NB- ARIMA. To fit discrete data to a continuous gamma distribution, a new framework, the transformed Gamma-ARIMA model, was proposed. By applying a mathematical transformation to discrete data, the series formation becomes more consistent, and the Gamma-ARIMA technique is successful on non-Gaussian discrete data sets.. Four different mathematical formulations were used, and the Enhanced Grey Wolf Optimizer (EGWO) algorithm was used to compare them. The results show that the square root transformation is the best using the No-U-Turn Sampler (NUTS) algorithm, and that the Bayesian estimation performance is robust and suitable for reliable inference and future predictions. Using an annual time series of the number of pulmonary Tuberculosis (TB) cases in Iraq, the results showed that the Poisson-ARIMA model outperformed the other models using Mean Square Error (MSE)and Mean Absolute Percentage Error (MAPE). Keywords: Non-Gaussian; Gamma-ARIMA; EGWO algorithm; Bayesian inference; Tuberculosis; Iraq.