Nonlinear Modeling And Forecasting

Based on a Santa Fe Institute and NATO sponsored workshop, this book brings together the ideas of leading researchers in the rapidly expanding, interdisciplinary field of nonlinear modeling in an attempt to stimulate the cross-fertilization of ideas and the search for unifying themes. The central theme of the workshop was the construction of nonlinear models from time-series data. Approaches to this problem have drawn from the disciplines of multivariate function approximation and neural nets, dynamical systems and chaos, statistics, information theory, and control theory. Applications have been made to economics, mechanical engineering, meteorology, speech processing, biology, and fluid dynamics. }The interdisciplinary field of nonlinear modeling has grown rapidly over the last decade due to the increasing availability of computer resources, which allows for the collection of increasingly large data sets and the analysis of the data sets with numerically intensive algorithms. In addition, the field has also grown with the increasing recognition of the ubiquity and importance of the effects of nonlinear dynamics in the natural and social sciences.Based on a Santa Fe Institute and NATO sponsored workshop, this book brings together the ideas of leading researchers in this rapidly expanding, interdisciplinary field in an attempt to stimulate the cross-fertilization of ideas and the search for unifying themes. The central theme of the workshop was the construction of nonlinear models from time-series data. Approaches to this problem have drawn from the disciplines of multivariate function approximation and neural nets, dynamical systems and chaos, statistics, information theory, and control theory. Applications have been made to economics, mechanical engineering, meteorology, speech processing, biology, and fluid dynamics.The papers included discuss various approaches to nonlinear multivariate function approximation, statistical issues in time-series analysis, invariants associated with chaotic attractors, and extimation of invariants. Finally, the last seven papers discuss applications to a variety of time-series data using nonlinear modeling and forecasting ideas developed by the authors themselves. }

Table of Contents:
Function Approximation; Tesselations and Dynamical Systems (Alistair I. Mees); Supervised Learning: A Theoretical Framework (Sara A. Solla); Prediction of Chaotic Time Series Using CNLS-Net-Example: The Mackey-Glass Equation (W. C. Mead, R. D. Jone, Y. C. Lee, C. W. Barnes, G. W. Flake, L. A. Lee, and M. K. ORourke); Forecasting with Weighted Maps (L. Stokbro and D. K. Umberger); Multivariate Function and Operator Estimation, Based on Smoothing Splines and Reproducing Kernels (Grace Wahba); Statistics; Optimal Estimation of Fractal Dimension (Richard L. Smith); Diagnostic Testing for Nonlinearity, Chaos, and General Dependence in Time-Series Data (W. A. Brock and S. M. Potter); Using Surrogate Data to Detect Nonlinearity in Time Series (James Theiler, Bryan Galdrikian, Andre Longtin, Stephen Eubank, and J. Doyne Farmer); Experiments in Modeling Nonlinear Relationships Between Time Series (Clive W.J. Granger and Timo Terasvirta); Analysis of Nonlinear Time Series (and Chaos) by Bispectral Methods (T. Subba Rao); Dynamical Systems; Local and Global Lyapunov Exponents on a Strange Attractor (Henry D. I. Abarbanel); Local Forecasting of High-Dimensional Chaotic Dynamics (Thomas P. Meyer and Norman H. Packard); A Dynamical Systems Approach to Modeling Input-Output Systems (Martin Casdagli); Identification and Filtering of Nonlinear Systems Using Canonical Variate Analysis (Wallace E. Larimore); Forecasting Probabilities with Neural Networks (Aviv Bergman, Peter Grassberger, and Thomas P. Meyer); Semantics and Thermodynamics (James P. Crutchfield); Use of Recurrence Plots in the Analysis of Time-Series Data (Matthew Koebbe and Gottfried Mayer-Kress); Application; Nonlinear Forecasts for the S&P Stock Index (Blake LeBaron); Predicting Sunspots and Exchange Rates with Connectionist Networks (Andreas S. Weigend, Bernardo A. Huberman, and David E. Rumelhart); Nonlinear Prediction of Speech Signals (Brent Townsend); Application of Nonlinear Prediction to Signal Separation (William W. Taylor); Application of Nonlinear Time-Series Models to Driven Systems (Norman F. Hunter Jr.); Periodic Saddle Orbits in Experimental Strange Attractors (Daniel P. Lathrop and Eric J. Kostelich); Memory-Based Approaches to Approximating C.

About the Author :
Martin Casdagli is currently working in the commercial sector. He received his Ph.D. in Mathematics from the University of Warwick and has subsequently held postdoctoral positions at the University of Arizona; Queen Mary College, London; and the Santa Fe Institute. Stephen Eubank is a cofounder of the Prediction Company in Santa Fe. He received his Ph.D. in Physics from the University of Texas at Austin and has subsequently held post-doctoral positions at the La Jolla Institute and at the Center for Nonlinear Studies and Theory Division at Los Alamos National Laboratory.