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Extracting Knowledge From Time Series

An Introduction to Nonlinear Empirical Modeling

  • Book
  • © 2010

Overview

Authors:
  1. Boris P. Bezruchko

    1. Saratov State University, Saratov, Russian Federation

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  2. Dmitry A. Smirnov

    1. Saratov Branch, V.A. Kotel'nikov Institute of Radio Engi, Russian Academy of Science, Saratov, Russian Federation

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    You can also search for this author in PubMed   Google Scholar

  • Useful as a self-study guide
  • Gives a modern approach and practical examples
  • Written by well known authors having made many contribution to the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Synergetics (SSSYN)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Models And Forecast

    1. Front Matter

      Pages 1-1
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    2. The Concept of Model. What is Remarkable in Mathematical Models

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 3-23

    3. Two Approaches to Modelling and Forecast

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 25-69

    4. Dynamical (Deterministic) Models of Evolution

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 71-125

    5. Stochastic Models of Evolution

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 127-147

  3. Modeling From Time Series

    1. Front Matter

      Pages 149-149
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    2. Problem Posing in Modelling from Data Series

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 151-158

    3. Data Series as a Source for Modelling

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 159-200

    4. Restoration of Explicit Temporal Dependencies

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 201-231

    5. Model Equations: Parameter Estimation

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 233-254

    6. Model Equations: Restoration of Equivalent Characteristics

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 255-273

    7. Model Equations: “Black Box” Reconstruction

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 275-308

    8. Practical Applications of Empirical Modelling

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 309-318

    9. Identification of Directional Couplings

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 319-348

    10. Outdoor Examples

      • Boris P. Bezruchko, Dmitry A. Smirnov
      Pages 349-388

  4. Back Matter

    Pages 389-407
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Keywords

About this book

Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phenomena, on more or less speci?c approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II re?ects our professional interests as physicists who spent much time to investigations in the ?eld of non-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is known for a long time as “system identi?cation” in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, non-stationary and noise-corrupted signals which are typical of real-world objects and phenomena) with relatively simple non-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s- ?ciently low order can exhibit non-trivial solutions that promise suf?ciently simple modelling of complex processes; according to the concepts of non-linear dynamics, chaotic regimes can be demonstrated already by a third-order non-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random in?uence (noise) or by a very high order of equations.

Reviews

From the reviews:

“Extracting knowledge from time series is a very neat title–it exactly encapsulates the topic which the authors hope to cover in this volume. … This is admirable, and the result is valuable. … This is overall a useful volume for providing an overview of the area … .” (Michael Small, Mathematical Reviews, Issue 2012 d)

“Another book on time-series! … it is a textbook for physicists and practitioners, and in this way of thought it is welcome. Its main purpose is to explain and illustrate how time series can be used to construct mathematical models for dynamical systems. … step by step the applications supports the presentation of the basic theoretical formulation.” (Guy Jumarie, Zentralblatt MATH, Vol. 1210, 2011)

Authors and Affiliations

  • Saratov State University, Saratov, Russian Federation

    Boris P. Bezruchko

  • Saratov Branch, V.A. Kotel'nikov Institute of Radio Engi, Russian Academy of Science, Saratov, Russian Federation

    Dmitry A. Smirnov

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