Long Memory Processes (1/fαType) in Human Coordination

Abstract

Consider the task of synchronizing the movement of one's limb to a periodic environmental signal. Using rescaled range analysis and the spectral maximum likelihood estimator, we establish that the experimental errors of human synchronization exhibit $1/f^{\alpha }$ type long memory where $\alpha$ is about 0.5, and that the underlying stochastic process can be modeled by fractional Gaussian noise. In addition, we provide a preliminary model of this phenomenon using stochastic delayed differential equations.