Non Linear Time Series Analysis with R

Nonlinear Time Series Analysis with R joins the chorus of voices recommending 'getting to know your data' as an essential preliminary evidentiary step in scientific inquiry. Time series are often highly fluctuating with a random appearance. Observed volatility is commonly attributed to exogenous random shocks to stable real-world systems. Consequently, investigators are driven to reproduce volatility with a variety of linear-stochastic and probabilistic methods. However, breakthroughs in nonlinear dynamics raise another possibility: Highly complex dynamics can emerge endogenously from astoundingly parsimonious deterministic models. Nonlinear Time Series Analysis (NLTS) is a collection of empirical tools that allow practitioners to diagnose whether observed data are most likely generated by stochastic or deterministic dynamics. In particular, practitioners can use NLTS in the attempt to reconstruct, characterize, and model real-world dynamics from a single time series or multiple causally-interactive time series. This information can be used, along with scientific principles and other expert information, to guide the specification of mechanistic models used to build theory or to support high-stakes public policy. Models used for public policy increasingly are subjected to formal government audit for how well they correspond with reality. The compatibility of audited models with NLTS-detected dynamics offers evidence of proper model specification. This book targets students and professionals in physics, engineering, biology, agriculture, and economics and other social sciences. Our major objectives are to put key concepts of NLTS-developed in the mathematical physics literature within the operational reach of non-mathematicians with limited knowledge of nonlinear dynamics; and in this way, to pave the way for NLTS to be adopted in the conventional empirical toolbox and core coursework of other disciplines. Consistent with modern trends in university instruction, the book makes readers active learners with hands-on computer experiments in \texttt{R} code directing them through NLTS methods. The computer code is explained in detail so that readers can adjust it for use in their own work. The book also provides readers with an explicit framework-condensed from sound empirical practices recommended in the literature that proposes a strategy for implementing NLTS in real-world data diagnostics. Practitioners become 'data detectives' accumulating hard empirical evidence directing scientific inquiry.