Dr. Matthijs Koopmans, professor of educational leadership, joined the faculty at Mercy College in 2011. Previously, he worked for several educational research organizations, including the Strategic Education Research Partnership Institute, Academy for Educational Development and Metis Associates. He has taught at several colleges in the greater New York metropolitan region (Hofstra University, York College/City University of New York, Adelphi University and Yeshiva University). As an independent contractor, he has conducted evaluations for MGT of America, Institute for Student Achievement, National Urban Technology Center and Newark Public Schools. In scholarship, his areas of focus are the application of complexity theory to education, cause and effect relationships, and the estimation of fractal patterns in time series data. This book pursues the latter interest, which stems from a belief that the effective application of principles of complexity theory in the social sciences should include attempts to extend conventional parametric models to the estimation of dynamical processes. He published his research in numerous peer-reviewed journals and continues to present his work at national and international scholarly conferences. He is a founding editor of the International Journal of Complexity in Education and serves on the editorial board of Nonlinear Dynamics, Psychology, and Life Sciences. He earned his Doctorate in 1988 from the Harvard Graduate School of Education.

Series Editor Introduction
Acknowledgments
About the Author
Chapter 1: Introduction
A. Limitations of Traditional Approaches
B. Long-Range Dependencies
C. The Search for Complexity
D. Plan of the Book
Chapter 2: Autoregressive Fractionally Integrated Moving Average or Fractional Differencing
A. Basic Results in Time Series Analysis
B. Long-Range Dependencies
C. Application of the Models to Real Data
D. Chapter Summary and Reflection
Chapter 3: Power Spectral Density Analysis
A. From the Time Domain to the Frequency Domain
B. Spectral Density in Real Data
C. Fractional Estimates of Gaussian Noise and Brownian Motion
D. Chapter Summary and Reflection
Chapter 4: Related Methods in the Time and Frequency Domains
A. Estimating Fractal Variance
B. Spectral Regression
C. The Hurst Exponent Revisited
D. Chapter Summary and Reflection
Chapter 5: Variations on the Fractality Theme
A. Sensitive Dependence on Initial Conditions
B. The Multivariate Case
C. Regular Long-Range Processes and Nested Regularity
D. The Impact of Interventions
Chapter 6: Conclusion
A. Benefits and Drawbacks of Fractal Analysis
B. Interpretation of Parameters in Terms of Complexity Theory
C. A Note About the Software and Its Use
References
Appendix
Index

This book 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.