Discrete-time, discrete-valued observable operator models. A tutorial

This tutorial gives a basic yet rigorous introduction to observable operator models (OOMs). OOMs are a recently discovered class of models of stochastic processes. They are mathematically simple in that they require only concepts from elementary linear algebra. The linear algebra nature gives rise to an efficient, consistent, unbiased, constructive learning procedure for estimating models from empirical data. The tutorial describes in detail the mathematical foundations and the practical use of OOMs for identifying and predicting discrete-time, discrete-valued processes, both for output-only and input-output systems