Analyzing Fractal Dynamics Employing R

Recent empirical studies from cognitive, social and biological psychology revealed the fractal properties of many psychological phenomena. Employing methodologies from time- and frequency-domain analyses enabled detecting persistent long-range dependencies in various psychological and behavioral time series. These very slowly decaying autocorrelations are known as I/f noise and typical for self similar long memory processes. This paper evaluated different estimators of long memory parameters commonly available in the open source statistical software R concerning their ability to distinguish between fractional Brownian motions and fractional Gaussian noises, stationary and nonstationary fractal processes, short and long memory series. The following procedures implemented in the R packages fractal and fracdiff were considered: PSD (hurstSpec), DFA, the Whittle method (FDWhittle), semiparametric estimators of Reisen (fdSperio) and Geweke & Porter-Hudak (fdGPH) as well as the approximate ML algorithm of Haslett and Raftery (fracdiff). The key finding of the study was that the performance of the methods strongly depends on the complexity of the underlying process and parameterizations. Since in empirical settings the true structure is never known, an elaborated strategy for the estimation of the long memory parameter d combining different techniques was developed and demonstrated on an empirical example.