Recurrence-Based Analyses

Sebastian Wallot - Leuphana University Lüneburg, Germany
Giuseppe Leonardi - University of Economics and Human Sciences, Poland

Volume: 197

Series:
Quantitative Applications in the Social Sciences

Other Titles in:
Quantitative/Statistical Research (General) | Research Methods for Politics & International Relations | Research Methods in Psychology

February 2025 | 136 pages | SAGE Publications, Inc

This book introduces techniques developed in physics and physiology for characterizing and analyzing patterns in time series data to a broad audience of social scientists. In contrast to time-series regression and related techniques, recurrence quantification analysis (RQA) has its background in chaos and nonlinear dynamical systems—theory arguably very relevant to social processes. The goal of Recurrence-Based Analyses is to introduce readers to these techniques that can characterize a system’s complexity, stability and instability, and conditions under which it transitions from one state to another. The authors illustrate concepts and techniques with relevant social science examples at different temporal scales: biweekly polling data on federal elections in Germany; daily values of three stock market indices; daily cases of SarsCov-19 in four countries during the pandemic; and second-by-second vocalizations of mothers and infants interacting recorded by motion cameras. This introduction to RQA serves as a useful supplement to undergraduate and graduate courses in computational social science, and also by researchers who seek new tools to address social scientific questions in new ways.

Series Editor Introduction

Acknowledgments

About the Authors

Acronyms and Notation

Chapter 1: What is Recurrence Analysis?

The Recurrence Plot

Deriving Recurrence Measures

Advantages and Limitations of Recurrence Analysis

Chapter 2: The Basics of Recurrence Analysis—Univariate RQA

Parameter Estimation

The Delay Parameter t

The Embedding Parameter m

The Radius Parameter e

Further Parameters

Summarizing RQA Outputs

Chapter 3: The Bi-Variate Case: Cross-Recurrence Quantification Analysis

Introduction to CRQA

Standardization

Alignment

The Cross-Recurrence Plot (CRP)

Using CRQA With Continuous Data: Stock Market Fluctuations

Using CRQA With Categorical Data

Chapter 4: The Diagonal-Wise Cross-Recurrence Profile (DCRP)

Diagonal-Wise Cross Recurrence Profiles (DCRP)

Building a Baseline by Means of Shuffling

Chapter 5: Windowed Recurrence Analysis

Introduction to Univariate Windowed Recurrence Analysis

Windowed Cross-Recurrence Analysis

Using Windowed Recurrence Analysis for Continuous Monitoring

Chapter 6: Multivariate Analysis: Multidimensional Recurrence Quantification Analysis (MdRQA)

Introduction to MdRQA

Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA)

An Example Using Multidimensional RQA on Political Polling Data

Chapter 7: Sample Analysis and Practicalities

Calculating General Parameters

Time Series Length

Computing Confidence Bounds Via Boot-Strapping

Parameter Exploration

Surrogate Analysis

Dealing With Multiple Recurrence-Measures

Chapter 8: Conclusion

Further Applications

Finding Software

A Final Note

References

Index

This book is a solid introduction to recurrence-based analysis. It is very accessible. The authors explain the basic elements in clear
language that most methodologically-oriented students will find understandable. The book is also surprisingly comprehensive for such an
introductory treatment.

Courtney Brown

Emory University

The authors provide a clear and concise introduction that makes an advanced topic accessible to a broad audience.

Clayton Webb

University of Kansas

This book provides an intuitive introduction to a topic with much potential for social science applications, but one whose daunting mathematical demands have made it inaccessible to most students and scholars.

David McDowall

University at Albany-SUNY

This book presents an advanced quantitative technique to social science researchers in a clear and precise manner, offering a perfect balance of technical depth and accessibility.

Duan Zhang

University of Denver

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