Universal Prediction Algorithms

22 Jul 2022 10:04

Given: a single time series, perhaps a very long one, from a stochastic process which is basically unknown; perhaps merely that it is stationary and ergodic.

Desired: a forecast which will converge on the best possible forecast, as the series becomes longer and longer. Or: the best possible forecast from within a fixed class of forecasting algorithms.

A solution is called a universal prediction algorithm because it applied equally to all the processes within the class, and is not tailored to any one of them.

This has connections to information theory (via universal compression algorithms), to the problem of finding Markovian representations and inference for Markov models, and to many other topics. Presumably they could be used for bootstrapping time series.

See also: Ergodic Theory; Learning in Games; Learning Theory; Low-Regret Learning; Machine Learning, Statistical Inference and Induction; Sequential Decisions Under Uncertainty; Time series