The Innovation Approach to the Identification of Nonlinear Causal Models in Time Series Analysis

Abstract

This paper shows how the Innovation approach developed by Wiener (1949), Kalman (1960) and Box and Jenkins (1970) has found wide application in modern nonlinear time series analysis. Nonlinear models, such as the chaos, stochastic or deterministic differential equation models, neural network models and nonlinear AR models developed in the last two decades are reviewed as useful causal models in time series analysis for nonlinear dynamic phenomena in many scientific fields. The merit of the use of the innovation approach in conjunction with these new models is pointed out. Further, the computational efficiency and advantage of RBF-AR models over RBF neural network models is demonstrated in real data analysis of EEG time series of subject s with epilepsy. The advantage of multivariate RBF-ARX models in the modeling of thermal power plants is also shown using numerical results.Key wordsInnovation approachmaximum likelihood methodnonlinear Kalman filterMarkov diffusion processPearson systemGamma distributed processstochastic differential equationschaosLocal Linearization schemeExpAR modelsRBF nearal networkRBF-ARF modelsRBF-ARX models