Parameter Estimation Based on Stacked Regression and Evolutionary Algorithms

A new parameter estimation algorithm which minimises the cross-validated prediction error for linear-in-the-parameter models is proposed based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear -in-the-parameter models using a criterion called the mean dispersion error (MDE) . Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm to produce a new parameter estimation algorithm which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.