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.

Variations on the Fractality Theme

Variations on the Fractality Theme

While the investigation of fractality may be used to address many areas of interest in complexity theory, there are other questions that also involve time series that it is decidedly ill equipped to address. One such question is the degree to which systemic turbulence can be predicted on the basis of small fluctuations at a previous point in time, also known as sensitivity to initial conditions, which is a primary concern of chaos theory. Chaos theory is a perspective that is also concerned with time series (Sprott, 2003), and therefore, it is of related interest to the discussion here. Below is a brief appreciation of the relevance of its insights. The reader may also have noticed that much of ...

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