Abstract
We study a new definition of a non-linear model of time series with hyperbolic secant function in a discrete time. The suggested model consist of two parts the first part is (linear) and the second part is (non-linear) which contains the hyperbolic secant function. We approximate this model to be linear by using the local linearization technique. We find the non-zero unique singular point that satisfies the non-linear variation equation, also stability of the non-zero unique singular point and the limit cycle if it exists of the suggested model.
Highlights
We study the non-linear models of time series with hyperbolic secant function
المقترح ABSTRACT We study a new definition of a non-linear model of time series with hyperbolic secant function in a discrete time
We find the non-zero unique singular point that satisfies the non-linear variation equation, stability of the non-zero unique singular point and the limit cycle if it exists of the suggested model
Summary
We study the non-linear models of time series with hyperbolic secant function. We find the non-zero unique singular point for the non-linear time series model with hyperbolic secant function, stability for the non-zero unique singular point and the limit cycle if it occurs. Definition 2.5: The non-linear variation (difference) equation b e xt p xt p zt , while z t is white noise and a1,..., ap ;b1,..., bp are the real constants(parameter), this model is invite as exponential autoregressive model of p order which is denoted by expAR(p) [5]. The suggested non–linear model: We will give the definition of a non-linear time series model with hyperbolic secant function of order p such as: xt [ai bi sec h(xt 1)]xt i zt (1). 2) if xt 1 0 , sec h(xt 1) 1, and the model is linear of order p p, such as: xt [ai bi ]xt i zt is linear. i 1
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