Summary: This paper shows how the innovation approach developed by N. Wiener [Extrapolation, interpolation and smoothing of stationary time series with engineering applications. Technol. Press MIT (1949; Zbl 0036.09705)], R. E. Kalman [A new approach to linear filtering and prediction problems. Trans. ASME, Ser. D. Basic Eng., 35–45 (1960)], and G. E. P. Box and G. M. Jenkins [Time series analysis: forecasting and control. (1970; Zbl 0249.62009)] has found wide applications 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 merits of the use of the innovation approach in conjunction with these new models are pointed out.
Further, the computational efficiency and advantages of RBF-AR models over RBF neural network models are demonstrated in real data analysis of EEG time series of subjects with epilepsy. The advantage of multivariate RBF-ARX models in the modeling of thermal power plants is also shown using numerical results.
For the entire collection see [Zbl 1051.86001].