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

Ioannis Papageorgiou, Ioannis Kontoyiannis

arXiv 2 Aug 2023 · Statistics — Methodology · publishedInternational Journal of Forecasting (2025) · 2 citations (OpenAlex)

arXiv:2308.00913 · PDF · DOI · OpenAlex · Extracted main text

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.

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120
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1R.S. Tsay (2005) Analysis of financial time series1.00085100%
2G.E.P. Box, G.M. Jenkins, G.C. Reinsel, and G.M. Ljung (2015) Time series analysis: Forecasting and control0.9416483%
3C.S. Wong and W.K. Li (2000) On a mixture autoregressive model0.92844100%
4H. Tong (1990) Non-linear time series: A dynamical system approach0.92843100%
5S. Makridakis, E. Spiliotis, and V. Assimakopoulos (2018) Statistical and machine learning forecasting methods: Concerns and ways forward0.8434375%
6I. Kontoyiannis, L. Mertzanis, A. Panotonoulou, I. Papageorgiou, and… (2022) Bayesian Context Trees: Modelling and exact inference for discrete time series0.84315560%
7H. Tong (2011) Threshold models in time series analysis – 30 years on0.84333100%
8H. Tong and K.S. Lim (1980) Threshold autoregression, limit cycles and cyclical data0.84333100%
9A. Alexandrov, K. Benidis, M. Bohlke-Schneider, V. Flunkert, J. Gast… (2020) GluonTS: Probabilistic and neural time series modeling in Python0.7373367%
10S. Chib and I. Jeliazkov (2001) Marginal likelihood from the Metropolis-Hastings output0.7373367%

Showing the top 10 of 120 scored citations.