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

arXiv: https://arxiv.org/abs/2308.00913 · HTML: https://mlsanity.com/paper/2308.00913/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 124 references that are in the map.
- First posted on arXiv 2 Aug 2023.

## Builds on (most cited first, 19 of 19)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [GRATIS: GeneRAting TIme Series with diverse and controllable characteristics](https://mlsanity.com/paper/1903.02787/) (2019)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Bayesian Context Trees: Modelling and exact inference for discrete time series](https://mlsanity.com/paper/2007.14900/) (2020)
- [State Space LSTM Models with Particle MCMC Inference](https://mlsanity.com/paper/1711.11179/) (2017)
- [VCBART: Bayesian trees for varying coefficients](https://mlsanity.com/paper/2003.06416/) (2020)
- [Posterior Representations for Bayesian Context Trees: Sampling, Estimation and Convergence](https://mlsanity.com/paper/2202.02239/) (2022)
- [Truly Bayesian Entropy Estimation](https://mlsanity.com/paper/2212.06705/) (2022)
- [Pattern-Based Analysis of Time Series: Estimation](https://mlsanity.com/paper/2005.00926/) (2020)
- [Change-point Detection and Segmentation of Discrete Data using Bayesian Context Trees](https://mlsanity.com/paper/2203.04341/) (2022)

## Built on by (most cited first, 2 of 2)

- [Soft Bayesian Context Tree Models for Real-Valued Time Series](https://mlsanity.com/paper/2601.11079/) (2026)
- [Variable Splitting Binary Tree Models Based on Bayesian Context Tree Models for Time Series Segmentation](https://mlsanity.com/paper/2601.16112/) (2026)

## Abstract (arXiv)

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.