Logistic smooth transition autoregressive model parameter estimation using Gauss Newton

Time series dataset analysis depends on now days datasets and the previous datasets. The forming process is called as Autoregressive. Time series dataset is possibly become the fluctuating dataset and forms the nonlinear model. The alternative forecasting model for the fluctuating datasets is mentioned as Smooth Transition Autoregressive (STAR). STAR model is defined by its transition function, STAR with logistic transition function is mentioned as Logistic Smooth Transition Autoregressive (LSTAR). LSTAR is a useful model that can be used to model the nonlinear datasets. By following the Autoregressive (AR) process, LSTAR is shaped with series of nonlinearity tests. The estimation of LSTAR parameter using Gauss-Newton method is an algorithm to minimize the sum of squared residue ε. Concept which underlies the technique is the analysis of Taylor’s chain that is applied to declare the original nonlinear equation in shape of linear approximation that is begin with minimizing the sum of squared residue using Nonlinear Least Square (NLS). Hence, the general LSTAR model and the parameter estimation using Gauss-Newton are determined.