Tikhonov-type regularization in local model for noisy chaotic time series prediction

Tikhonov-type regularization method for noisy chaotic time series prediction is investigated. The current regularized local prediction method is interpreted as one kind of filter factors to decrease the variance of the predictor. One drawback in the interpretation is the ignorance of the random noise in coefficient matrix, another drawback is the relationship between the regularization parameter and the noise condition is not clearly explained, so the determination of regularization parameter has to resort to some techniques such as cross validation. In this study, local linear model is studied from the perceptive of the errors-in-variables (EIV) modeling, and the predictor is designed by considering the noise both in coefficient matrix and right-hand side. The optimal solution can be obtained by second order convex program (SOCP) if given a perturbation bound of the noise, and the solution can be reformulated as a form of Tikhonov regularization, and it will be shown how regularization parameter is related to the Frobenius norm of the noise containing in coefficient matrix and right-hand side. Two demonstrations are presented to show the validity of the results.