Abstract

Building on the context-tree weighting (CTW) circle of ideas, we introduce a collection of statistical ideas and algorithmic tools for modelling and performing exact inference with both discrete and real-valued time series. For discrete time series, we describe a novel Bayesian framework based on variable-memory Markov chains, called Bayesian Context Trees (BCT). A general prior structure is introduced, and a collection of methodological and algorithmic tools is developed, allowing for efficient, exact Bayesian inference. The proposed approach is then extended to real-valued time series, where it is employed to develop a general hierarchical Bayesian framework for building mixture models based on context trees. Again, effective computational tools are developed, allowing for efficient, exact Bayesian inference. The proposed methods are found to outperform several state-of-the-art techniques on both simulated and real-world data from a wide range of applications. This is joint work with Ioannis Kontoyiannis.