How did Norbert Wiener apply automata to prediction from time-series data?

Norbert Wiener applied automata to prediction by integrating statistical methods into control theory, allowing deterministic machines to process and extrapolate from random data. While traditional automata were viewed as strictly logical, non-probabilistic devices, Wiener demonstrated that they could be programmed to predict future values of a stationary time series.12

His approach involved several key mathematical components:
* Linearity Restriction: Wiener restricted the predicted value to a linear combination of the system's past and present values.2
* Optimization: By specifying an algorithm to determine the coefficients of this linear combination, he enabled the automaton to minimize the error between the predicted and actual future values.21
* Environmental Interaction: This allowed an automaton to be placed in a naturalistic environment—such as one involving atmospheric pressure or particle movement—to sense and react to random phenomena.21

This work, developed alongside his research on cybernetics, provided the theoretical foundation for technologies like guided missiles, radar-controlled aircraft, and automated navigation systems, where machines use input data to correct their paths in real time.231