Tenets and Methods of Fractal Analysis (1/f Noise)

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (β), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?