Stability study of some nonlinear time series models with application

Abstract

In this research, the stability of time series models, nine in general, were studied. The stability of some nonlinear time series models was also studied using Lagrange's method and the results compared. The time series for seasonal allergies were studied. For this series, several non-linear mathematical models were built, including the seasonal model using transformation (natural logarithm), second-order exponential model and polynomial model. The stability of the above models was determined using the aforementioned method and through comparisons. The above models show that the combined seasonal model is the best-suggested model to represent the chain future value of a disease for one year, which were predicted using a seasonal model.