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Using Time Series to Analyze Long Range Fractal Patterns

Using Time Series to Analyze Long Range Fractal Patterns

First Edition

January 2021 | 112 pages | SAGE Publications, Inc
Using Time Series to Analyze Long Range Fractal Patterns presents methods for describing and analyzing dependency and irregularity in long time series. Irregularity refers to cycles that are similar in appearance, but unlike seasonal patterns more familiar to social scientists, repeated over a time scale that is not fixed. Until now, the application of these methods has mainly involved analysis of dynamical systems outside of the social sciences, but this volume makes it possible for social scientists to explore and document fractal patterns in dynamical social systems. Author Matthijs Koopmans concentrates on two general approaches to irregularity in long time series: autoregressive fractionally integrated moving average models, and power spectral density analysis. He demonstrates the methods through two kinds of examples: simulations that illustrate the patterns that might be encountered and serve as a benchmark for interpreting patterns in real data; and secondly social science examples such a long range data on monthly unemployment figures, daily school attendance rates; daily numbers of births to teens, and weekly survey data on political orientation. Data and R-scripts to replicate the analyses are available in an accompanying website.
Chapter 1: Introduction
Chapter 2: Autoregressive Fractionally Integrated Moving Average (ARFIMA) or Fractional Differencing
Chapter 3: Power Spectral Density Analysis (PSDA)
Chapter 4: Related Methods in the Time and Frequency Domain
Chapter 5: Variations on the Fractality Theme
Chapter 6: Conclusion
Online Appendix

This is coherent treatment of fractal time-series methods that will be exceptionally useful.

Courtney Brown
Emory University

Each analysis is explained, and also the differences between the analyses are explained in a systematic way.

Mustafa Demir
State University of New York, Plattsburgh

This volume offers a nice introduction to the various methods that can be used to discuss long range dependencies in univariate time series data. Koopmans makes a compelling case for these methods and offers clear exposition

Clayton Webb
University of Kansas

This amazing book provides a concise and solid foundation to the study of long-range process. In a short volume, the author successfully summarizes the theory of fractal approaches and provides many interesting and convincing examples. I highly recommend this book.

I-Ming Chiu
Rutgers University-Camden

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