Estimation and interpretation of 1/falpha noise in human cognition

Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence of the presence of a particular form of long-range serial dependence known as 1/f noise. It has been argued that long-range dependence has been largely ignored in mainstream cognitive psychology even though it accounts for a substantial proportion of variability in behavior (see, e.g., Gilden, 1997, 2001). In this article, we discuss the defining characteristics of long-range dependence and argue that claims about its presence need to be evaluated by testing against the alternative hypothesis of short-range dependence. For the data from three experiments, we accomplish such tests with autoregressive fractionally integrated moving-average time series modeling. We find that long-range serial dependence in these experiments can be explained by any of several mechanisms, including mixtures of a small number of short-range processes.