Studying the Stability of Some Non-Linear Time Series Models with Application

In this paper we study the stability of time series models in general, and for some non-linear time series models as a special case. Lagrange method to find the stability of non-linear models has been given.
The Leishmaniasis time series was studied and modeled by different non-linear models such as, seasonal ARIMA model by using the logarithmic transformation, exponential model of order two and the polynomial model. The stability of all such models by the above method has been obtained. From the comparison we find that the SARIMA is the best among all such models which we used for forecasting one year ago.