Algorithmic Information Forecastability
This work addresses the fundamental issue of determining which data can be reliably forecast, which is incremental as it builds on existing algorithmic information theory concepts.
The paper tackles the problem of measuring forecastability in time series and labeled data using algorithmic information theory, proposing three categories (oracle, precise, probabilistic) to classify prediction accuracy based on data properties.
The outcome of all time series cannot be forecast, e.g. the flipping of a fair coin. Others, like the repeated {01} sequence {010101...} can be forecast exactly. Algorithmic information theory can provide a measure of forecastability that lies between these extremes. The degree of forecastability is a function of only the data. For prediction (or classification) of labeled data, we propose three categories for forecastability: oracle forecastability for predictions that are always exact, precise forecastability for errors up to a bound, and probabilistic forecastability for any other predictions. Examples are given in each case.