312 pages, 91 b/w illustrations
Nonlinear Time Series Analysis with R provides a practical guide to emerging empirical techniques allowing practitioners to diagnose whether highly fluctuating and random appearing data are most likely driven by random or deterministic dynamic forces. It joins the chorus of voices recommending 'getting to know your data' as an essential preliminary evidentiary step in modelling. Time series are often highly fluctuating with a random appearance. Observed volatility is commonly attributed to exogenous random shocks to stable real-world systems. However, breakthroughs in nonlinear dynamics raise another possibility: highly complex dynamics can emerge endogenously from astoundingly parsimonious deterministic nonlinear models. Nonlinear Time Series Analysis (NLTS) is a collection of empirical tools designed to aid practitioners detect whether stochastic or deterministic dynamics most likely drive observed complexity. Practitioners become 'data detectives' accumulating hard empirical evidence supporting their modelling approach.
This book is targeted to professionals and graduate students in engineering and the biophysical and social sciences. Its major objectives are to help non-mathematicians – with limited knowledge of nonlinear dynamics – to become operational in NLTS; and in this way to pave the way for NLTS to be adopted in the conventional empirical toolbox and core coursework of the targeted disciplines. Consistent with modern trends in university instruction, the book makes readers active learners with hands-on computer experiments in R code directing them through NLTS methods and helping them understand the underlying logic. The computer code is explained in detail so that readers can adjust it for use in their own work. Nonlinear Time Series Analysis with R also provides readers with an explicit framework – condensed from sound empirical practices recommended in the literature – that details a step-by-step procedure for applying NLTS in real-world data diagnostics.
1: Why Study Nonlinear Time Series Analysis?
2: Linear and Nonlinear Dynamic Behavior
3: Phase Space Reconstruction
4: The Features of Chaos
5: Data Pre-processing
6: Surrogate Data Testing
7: Phenomenological Modeling
List of Symbols
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Ray Huffaker is a professor in Agricultural and Biological Engineering at the University of Florida. He specializes in nonlinear time series analysis, biological and economic modelling of water and other ecosystem resources, economic dynamics, and natural resource and environmental law. He has taught graduate courses in nonlinear data diagnostics, mathematical optimization techniques, economic dynamics, and micro- and macroeconomic analysis; and undergraduate courses in natural resource and environmental law. He holds bachelor degrees in economics and Italian literature, a Ph.D. in agricultural economics, and a J.D. in law all from the University of California at Davis.
Marco Bittelli received the degree in Agricultural Sciences from the University of Bologna, Italy, and a M.S. and a Ph.D. degree in Soil Physics from Washington State University, USA. He spent one year as a postdoctoral scientist in the Physics Department at the University of Heidelberg, Germany. He is associate professor at the University of Bologna, where he teaches soil and environmental physics, hydrological modelling, philosophy of science and scientific methods courses, both at the undergraduate and graduate level.
Rodolfo Rosa received a degree in physics in 1968 and in philosophy in 1977. From 1969 to 1992, he was a researcher at the National Research Council-IMM Institute in Bologna. From 1992 to 2014 he was professor at the Faculty of Statistics at the University of Bologna, where he taught courses on Statistics for Experimental Research, Chaos and Complexity, Probability and Stochastic Processes. His research interests include Monte Carlo methods applied to atomic interactions in matter, statistical mechanics, organization of genetic information in coding sequences of DNA, philosophy of science, and chaos theory.