How do people predict a random walk? Lessons for models of human cognition

Repeated forecasts of changing values are a key aspect of many everyday tasks, from predicting the weather to financial markets. A particularly simple and informative instance of such fluctuating values are random walks: sequences in which each point is a random movement from only its preceding value, unaffected by any previous points. Moreover, random walks often yield basic rational forecasting solutions in which predictions of new values should repeat the most recent value, and hence replicate the properties of the original series. In previous experiments, however, we have found that human forecasters do not adhere to this standard, showing systematic deviations from the properties of a random walk such as excessive volatility and extreme movements between subsequent predictions. We suggest that such deviations reflect general statistical signatures of human cognition displayed across multiple tasks, offering a window into underlying cognitive mechanisms. Using these deviations as new criteria, we here explore several cognitive models of forecasting drawn from various approaches developed in the existing literature, including Bayesian, error-based learning, autoregressive and sampling mechanisms. These models are contrasted with human data from two experiments to determine which best accounts for the particular statistical features displayed by participants. We find support for sampling models in both aggregate and individual fits, suggesting that these variations are attributable to the use of inherently stochastic prediction systems. We thus argue that variability in predictions is primarily driven by computational noise within the decision making process, rather than "late" noise at the output stage.