Generalized Nonlinear Irreducible Auto-Correlation and Its Applications in Nonlinear Prediction Models Identification

摘要

There is still an obstacle to prevent neural network from wider and more effective applications, i.e., the lack of effective theories of models identification. Based on information theory and its generalization, this paper introduces a universal method to achieve nonlinear models identification. Two key quantities, which are called nonlinear irreducible auto-correlation (NIAC) and generalized nonlinear irreducible auto-correlation (GNIAC), are defined and discussed. NIAC and GNIAC correspond with intrinstic irreducible auto-(dependency) (IAD) and generalized irreducible auto-(dependency) (GIAD) of time series respectively. By investigating the evolving trend of NIAC and GNIAC, the optimal auto-regressive order of nonlinear auto-regressive models could be determined naturally. Subsequently, an efficient algorithm computing NIAC and GNIAC is discussed. Experiments on simulating data sets and typical nonlinear prediction models indicate remarkable correlation between optimal auto-regressive order and the highest order that NIAC-GNIAC have a remarkable non-zero value, therefore demonstrate the validity of the proposal in this paper.