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.

Autoregressive Fractionally Integrated Moving Average or Fractional Differencing

Autoregressive Fractionally Integrated Moving Average or Fractional Differencing

As argued in the previous chapter, the aggregation of data across the time spectrum to create snapshots of what goes on may leave important aspects of the behavior of interest unattended. This chapter discusses time series analysis as an effective way to address that problem, focusing on time series that display irregular patterns of variability across the time spectrum. The chapter starts with an overview of some of the basic insights of traditional time series analysis, and within that conceptual framework, there will be a further discussion of the use of time series analysis to estimate irregular long-range patterns in the data. An alternative approach to such data, PSDA, will be presented in Chapter 3.

A. Basic ...

  • Loading...
locked icon

Sign in to access this content

Get a 30 day FREE TRIAL

  • Watch videos from a variety of sources bringing classroom topics to life
  • Read modern, diverse business cases
  • Explore hundreds of books and reference titles