The Bayesian Context Trees State Space Model for time series modelling and forecasting

TL;DR

This paper introduces a hierarchical Bayesian framework called BCT-X for flexible, interpretable time series modeling and forecasting, capable of incorporating various base models and enabling online inference, with applications in finance.

Contribution

The paper presents the BCT-X framework, a novel hierarchical Bayesian approach that combines tree-based mixture models with arbitrary base models for improved time series analysis.

Findings

BCT-X effectively models volatility asymmetries in financial data.

The framework outperforms existing methods in forecasting accuracy.

Algorithms support efficient online Bayesian inference.

Abstract

A hierarchical Bayesian framework is introduced for developing tree-based mixture models for time series, partly motivated by applications in finance and forecasting. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. At the bottom level, a different, arbitrary base model is associated with each state. This defines a very 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 the BCT-X framework. Appropriate algorithmic tools are described, which allow for effective and efficient Bayesian inference and learning; these algorithms can be updated sequentially, facilitating online forecasting. The utility of the general framework is illustrated in the particular instances when AR or ARCH models are used as base models. The latter results in a mixture model that offers a powerful way of modelling the well-known volatility asymmetries in financial data, revealing a novel, important feature of stock market index data, in the form of an enhanced leverage effect. In forecasting, the BCT-X methods are found to outperform several state-of-the-art techniques, both in terms of accuracy and computational requirements.