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Mathematical Model for Handling Unstable Time Series by Using a Linear Approximation Technique

Time series are typically built on basic assumptions that include stationarity, linearity and normality. The three characteristics are crucial for estimating and building time series models. Studies on time series include these assumptions. To deal with unstable time series that are based on its basis, mathematical models that are suitable for such series are adopted in this study. A nonlinear self-regression model, called the rational model, is proposed. This model is a fraction in which the numerator is the complete sine function and the denominator is an exponential self-regression model. The fixed point and limit cycle of the model are simulated and determined, and its stability is studied using a linear approximation technique.