Abstract
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/fnoise. 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.
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Preparation of this article was supported by NIMH Grant R37-MH44640, NIA Grant R01-AG17083, and NIMH Grant K05-MH01891. We thank David Gilden for helpful discussions and for sending us the data from his spatial estimation experiment (Gilden, 2001, p. 48).
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Wagenmakers, EJ., Farrell, S. & Ratcliff, R. Estimation and interpretation of 1/fα noise in human cognition. Psychonomic Bulletin & Review 11, 579–615 (2004). https://doi.org/10.3758/BF03196615
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DOI: https://doi.org/10.3758/BF03196615