# Multivariate Bayesian Structural Time Series Model

arXiv: https://arxiv.org/abs/1801.03222 · HTML: https://mlsanity.com/paper/1801.03222/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2018.

## Built on by (most cited first, 11 of 11)

- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
- [Ti-MAE: Self-Supervised Masked Time Series Autoencoders](https://mlsanity.com/paper/2301.08871/) (2023)
- [BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition](https://mlsanity.com/paper/2308.14906/) (2023)
- [Masked Bayesian Neural Networks : Theoretical Guarantee and its Posterior Inference](https://mlsanity.com/paper/2305.14765/) (2023)
- [A Temporally Disentangled Contrastive Diffusion Model for Spatiotemporal Imputation](https://mlsanity.com/paper/2402.11558/) (2024)
- [DGCformer: Deep Graph Clustering Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2405.08440/) (2024)
- [Spike and slab Bayesian sparse principal component analysis](https://mlsanity.com/paper/2102.00305/) (2021)
- [Respecting Time Series Properties Makes Deep Time Series Forecasting Perfect](https://mlsanity.com/paper/2207.10941/) (2022)
- [Robust Iterative Learning Hidden Quantum Markov Models](https://mlsanity.com/paper/2510.23237/) (2025)
- [Linear Iterative Feature Embedding: An Ensemble Framework for Interpretable Model](https://mlsanity.com/paper/2103.09983/) (2021)
- [The mbsts package: Multivariate Bayesian Structural Time Series Models in R](https://mlsanity.com/paper/2106.14045/) (2021)

## Abstract (arXiv)

This paper deals with inference and prediction for multiple correlated time series, where one has also the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for the time-series, Bayesian tools are used for model fitting, prediction, and feature selection, thus extending some recent work along these lines for the univariate case. The Bayesian paradigm in this multivariate setting helps the model avoid overfitting as well as capture correlations among the multiple time series with the various state components. The model provides needed flexibility to choose a different set of components and available predictors for each target series. The cyclical component in the model can handle large variations in the short term, which may be caused by external shocks. We run extensive simulations to investigate properties such as estimation accuracy and performance in forecasting. We then run an empirical study with one-step-ahead prediction on the max log return of a portfolio of stocks that involve four leading financial institutions. Both the simulation studies and the extensive empirical study confirm that this multivariate model outperforms three other benchmark models, viz. a model that treats each target series as independent, the autoregressive integrated moving average model with regression (ARIMAX), and the multivariate ARIMAX (MARIMAX) model.