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

Monday, November 12, 2001 - 2:00pm - 3:00pm
Keller 3-180
Tohru Ozaki (The Institute of Statistical Mathematics)
Joint work with J.C.Jimenez (Institute of Cybernetics, Mathematics and Physics, Cuba) and H. Peng (Central South University, Changsha 410083, P. R. China. (Currently a visiting researcher at the Institute of Statistical Mathematics,

This paper tries to revive the innovation approach developed by Wiener, Kalman and Box-Jenkins, for modern nonlinear time series analysis, predictions and simulations. The nonlinear models, such as 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. Merit of the use of innovation approach together with these new models embeded in nonlinear Kalman filtering framework is pointed out. Further, computational efficiency and an advantage of RBF-AR models over RBF neural network models is demonstrated in real data analysis of epilepsy EEG time series. Extension of the innovation approach to the analysis of spatial time series such as meteorological data or fMRI data in brain science is also discussed.