Tetiana Stadnytska, University of Heidelberg, GermanySimone Braun, University of Heidelberg, GermanyJoachim Werner, University of Heidelberg, Germany

Abstract: 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 1/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.