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
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | R.S. Tsay (2005) Analysis of financial time series | 1.000 | 8 | 5 | 100% |
| 2 | G.E.P. Box, G.M. Jenkins, G.C. Reinsel, and G.M. Ljung (2015) Time series analysis: Forecasting and control | 0.941 | 6 | 4 | 83% |
| 3 | C.S. Wong and W.K. Li (2000) On a mixture autoregressive model | 0.928 | 4 | 4 | 100% |
| 4 | H. Tong (1990) Non-linear time series: A dynamical system approach | 0.928 | 4 | 3 | 100% |
| 5 | S. Makridakis, E. Spiliotis, and V. Assimakopoulos (2018) Statistical and machine learning forecasting methods: Concerns and ways forward | 0.843 | 4 | 3 | 75% |
| 6 | I. Kontoyiannis, L. Mertzanis, A. Panotonoulou, I. Papageorgiou, and… (2022) Bayesian Context Trees: Modelling and exact inference for discrete time series | 0.843 | 15 | 5 | 60% |
| 7 | H. Tong (2011) Threshold models in time series analysis – 30 years on | 0.843 | 3 | 3 | 100% |
| 8 | H. Tong and K.S. Lim (1980) Threshold autoregression, limit cycles and cyclical data | 0.843 | 3 | 3 | 100% |
| 9 | A. Alexandrov, K. Benidis, M. Bohlke-Schneider, V. Flunkert, J. Gast… (2020) GluonTS: Probabilistic and neural time series modeling in Python | 0.737 | 3 | 3 | 67% |
| 10 | S. Chib and I. Jeliazkov (2001) Marginal likelihood from the Metropolis-Hastings output | 0.737 | 3 | 3 | 67% |
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