A modified nonparametric estimation and prediction of chaotic time series with known ergodic distribution - Maquiling, Rene U. (MSU Research Journal: official publication of the Research and Development Center Mindanao State University, General Santos City, 2002)
This study deals with the problem of estimating and predicting a given chaotic time series, when its ergodic distribution is known, using local polynomial regression, specifically, local cubic estimators. The following steps are done: 1) chaotic time series is estimated using local cubic estimator; 2) predict (n +h) points of this series; 3) evaluate its efficiency by getting the MSE of the result. The result show: 1) the prediction of a given chaotic time series is possible using ergodic distribution as a substitute for the kernel of the existing estimators; 2) the validity of the ergodic distribution as a kernel to the usual existing kernel (Gaussians); 3) the number of data affects the reliability of the predicted values.