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


  • Diniz, Ana
  • Barreiros, João
  • Crato, Nuno


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.

Suggested Citation

  • Diniz, Ana & Barreiros, João & Crato, Nuno, 2012. "A new model for explaining long-range correlations in human time interval production," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1908-1919.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1908-1919 DOI: 10.1016/j.csda.2011.09.027

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    References listed on IDEAS

    1. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    2. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
    3. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2676-2692, November.
    4. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
    5. Beran, Jan & Schützner, Martin & Ghosh, Sucharita, 2010. "From short to long memory: Aggregation and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2432-2442, November.
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