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 (please see www.marco.bittelli.com). 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 details a step-by-step procedure for applying NLTS in real-world data diagnostics.

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 (please see www.marco.bittelli.com). 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 details a step-by-step procedure for applying NLTS in real-world data diagnostics.

Random process analysis (RPA) is used as a mathematical model in physics, chemistry, biology, computer science, information theory, economics, environmental science, and many other disciplines. Over time, it has become more and more important for the provision of computer code and data sets. This book presents the key concepts, theory, and computer code written in R, helping readers with limited initial knowledge of random processes to become confident in their understanding and application of these principles in their own research. Consistent with modern trends in university education, the authors make readers active learners with hands-on computer experiments in R code directing them through RPA methods and helping them understand the underlying logic. Each subject is illustrated with real data collected in experiments performed by the authors or taken from key literature. As a result, the reader can promptly apply the analysis to their own data, making this book an invaluable resource for undergraduate and graduate students, as well as professionals, in physics, engineering, biophysical and environmental sciences, economics, and social sciences.

Random process analysis (RPA) is used as a mathematical model in physics, chemistry, biology, computer science, information theory, economics, environmental science, and many other disciplines. Over time, it has become more and more important for the provision of computer code and data sets. This book presents the key concepts, theory, and computer code written in R, helping readers with limited initial knowledge of random processes to become confident in their understanding and application of these principles in their own research. Consistent with modern trends in university education, the authors make readers active learners with hands-on computer experiments in R code directing them through RPA methods and helping them understand the underlying logic. Each subject is illustrated with real data collected in experiments performed by the authors or taken from key literature. As a result, the reader can promptly apply the analysis to their own data, making this book an invaluable resource for undergraduate and graduate students, as well as professionals, in physics, engineering, biophysical and environmental sciences, economics, and social sciences.

This innovative study presents concepts and problems in soil physics, and provides solutions using original computer programs. It provides a close examination of physical environments of soil, including an analysis of the movement of heat, water and gases. The authors employ the programming language Python, which is now widely used for numerical problem solving in the sciences. In contrast to the majority of the literature on soil physics, this text focuses on solving, not deriving, differential equations for transport. Using numerical procedures to solve differential equations allows the solution of quite difficult problems with fairly simple mathematical tools. Numerical methods convert differential into algebraic equations, which can be solved using conventional methods of linear algebra. Each chapter introduces a soil physics concept, and proceeds to develop computer programs to solve the equations and illustrate the points made in the discussion. Problems at the end of each chapter help the reader practise using the concepts introduced. The text is suitable for advanced undergraduates, graduates and researchers of soil physics. It employs an open source philosophy where computer code is presented, explained and discussed, and provides the reader with a full understanding of the solutions. Once mastered, the code can be adapted and expanded for the user's own models, fostering further developments. The Python tools provide a simple syntax, Object Oriented Programming techniques, powerful mathematical and numerical tools, and a user friendly environment.

This innovative study presents concepts and problems in soil physics, and provides solutions using original computer programs. It provides a close examination of physical environments of soil, including an analysis of the movement of heat, water and gases. The authors employ the programming language Python, which is now widely used for numerical problem solving in the sciences. In contrast to the majority of the literature on soil physics, this text focuses on solving, not deriving, differential equations for transport. Using numerical procedures to solve differential equations allows the solution of quite difficult problems with fairly simple mathematical tools. Numerical methods convert differential into algebraic equations, which can be solved using conventional methods of linear algebra. Each chapter introduces a soil physics concept, and proceeds to develop computer programs to solve the equations and illustrate the points made in the discussion. Problems at the end of each chapter help the reader practise using the concepts introduced. The text is suitable for advanced undergraduates, graduates and researchers of soil physics. It employs an open source philosophy where computer code is presented, explained and discussed, and provides the reader with a full understanding of the solutions. Once mastered, the code can be adapted and expanded for the user's own models, fostering further developments. The Python tools provide a simple syntax, Object Oriented Programming techniques, powerful mathematical and numerical tools, and a user friendly environment.