Seminar: "Bayesian inference with variable-memory models for times series"

AUEB STATISTICS SEMINAR SERIES 2023-24

Ioannis Kontoyiannis (Professor | Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK)

Bayesian inference with variable-memory models for times series

ROOM Troias Amphitheater

ABSTRACT

A hierarchical Bayesian framework is introduced for developing rich mixture models for real-valued time series, partly motivated by important applications in financial time series analysis. At the top level, meaningful discrete states are identified and described as a discrete context-tree model. At the bottom level, a different, arbitrary model for real-valued time series – a base model – is associated with each state. This defines a general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. We call this the Bayesian Context Trees State Space Model (or BCT-X) framework. Efficient algorithms are introduced that allow for effective, exact Bayesian inference, and which can be updated sequentially, facilitating effective forecasting. The utility of the general framework is illustrated on both simulated and real-world data. The BCT-X methods are found to outperform state-of-the-art techniques both in terms of accuracy and computational requirements. Of particular interest is our finding that the BCT-X framework revealed novel, natural structure present in financial data, in the form of an enhanced leverage effect that had not been identified before.

This is joint work with Ioannis Papageorgiou.

(Presentations pdf can be found here)