Nonlinear system identification

The prediction of a single observable time series has been achieved with reasonable accuracy and duration for the nonlinear systems developed by Rossler and Lorenz. Based on Takens\u27 Delay-vector Space, an artificial system has been generated using a polynomial least squares technique that includes all possible fifth order combinations of the vectors in the delay space. Furthermore, an optimum shift value has been shown to exist, such that any deviation decreases the accuracy and stability of the prediction. Additionally, an augmented form of the autocorrelation function, similar to the delay vector expansion, has been investigated. The first inflection of this correlation, typically in the dimension of the system, tends to coincide with the optimum shift value required for the best prediction. This method has also been utilized in conjunction with the Grassberger-Procaccia Distance correlation function to accurately determine the fractal dimension of the systems being investigated