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.
As in any time series analysis, there are generally three reasons why one would like to estimate fractal patterns. The first is to make statistical corrections for unwanted sources of nonrandom variability, the second is to estimate in what way given observations in a time series depend on previous observations, and the third is to improve forecasting the behavior of interest into the future with greater reliability. The techniques described in this book are pertinent to each of these three cases, although the focus of the book is on the detection of fractality as a phenomenon of substantive interest. Ever since Mandelbrot’s (1997) early work in this area, fractals have spoken to the imagination of many because they provide models for a built-in ...