A new model for explaining long-range correlations in human time interval production

Time series displaying long-range correlations have been observed in numerous fields, such as biology, psychology, hydrology, and economics, among others. For rhythmic movements such as tapping tasks, the Wing–Kristofferson model offers a decomposition of the inter-response intervals based on a cognitive component and on a motor component. It has been suggested that the cognitive component should be modeled as a long-memory process and the motor component should be treated as a white noise process. Some probabilistic explanations for long-range dependences have been proposed, such as the aggregation of short-memory processes, the renewal-reward processes, and the error-duration processes. A new approach to the Wing–Kristofferson model which provides insights into the origin of long memory based on regime-switching processes is proposed. Under some assumptions, the autocorrelation function and the spectral density function of the model are obtained. Furthermore, an estimator of the parameters based on the maximization of the frequency-domain representation of the likelihood function is proposed. A simulation study evaluating the sample properties of this estimator is performed. Finally, an experimental study involving tapping tasks with two target frequencies is presented.