Can People Predict Chaotic Sequences?

Abstract

Previous studies suggesting that people predict chaotic sequences better than chance have not discriminated between sensitivity to nonlinear determinism and facilitation using autocorrelation. Since prediction accuracy declines with increases in the look-ahead window in both cases, a decline in prediction accuracy does not imply chaos sensitivity. To overcome this problem, phase-randomized surrogate time series are used as a control. Such series have the same linear properties as the original chaotic sequence but contain no nonlinear determinism, i.e. chaos. In the experimental task, using a chaotic Hénon attractor, participants viewed the previous eight days temperatures and then predicted temperatures for the next four days, over 120 trials. The control group experienced a sample from a corresponding phase-randomized surrogate series. Both time series were linearly transformed to provide a realistic temperature range. A transformation of the correlation between observed and predicted values decreased over days for the chaotic time series, but remained constant and high for the surrogate series. The interaction between the days and series factors was statistically significant, suggesting that people are sensitive to chaos, even when the autocorrelation functions and power spectra of the control and experimental series are identical. Implications for the psychological assessment of individual differences in human prediction are discussed.