Nonlinear Autoregressive Model for Stability and Prediction

Abstract

A proposed nonlinear autoregressive model was employed to predict daily new COVID-19 infections in Iraq. This model was applied to actual COVID-19 data from 3 months in 2022 and met the stability criteria set by the proposed nonlinear regression model, based on a model developed by Japanese scientist Ozaki. The primary objective of the article was to examine the stability of this proposed nonlinear time series model, aimed at assessing the model’s stability and determining its stability conditions. To achieve this, the article applied Ozaki’s method to convert the nonlinear model, which depends on a singular point, into a linear model that fulfills the stability conditions required for the study. The approximation method helped identify the singular point, its stability conditions, and the limit cycle of the proposed model. The article also presented numerical case studies that satisfied the mathematical criteria for finding the singular point and its stability conditions. The findings indicated that such numerical case studies meeting stability conditions exist when the nonlinear function is decreasing, as illustrated in both Ozaki’s model and the proposed model. The proposed model was applied to COVID-19 data from Iraq over a 3-month period in 2022. This data was transformed into a stable form, and a Python program used the converted real data and proposed model to estimate the real parameters of the first-order model, fulfilling the established stability conditions and forecasting future new cases of the disease, which was the research’s main goal. The statistical criteria used in the fifth paragraph of the research are the Akaike information criterion (AIC), Bayesian information criterion (BIC), and normalized Bayesian information criterion (NBIC).