Bayesian Structural Time Series
Bayesian Structural Time Series Model · Also known as: BSTS, Bayesian Yapısal Zaman Serisi (BSTS), bayesian state-space model, causal impact model
Bayesian Structural Time Series (BSTS) is a state-space modelling framework, introduced by Scott and Varian (2014), that decomposes a time series into additive components — trend, seasonality, and regression — and estimates them jointly through Bayesian inference. It underpins Google's CausalImpact library and is a powerful tool for both forecasting and counterfactual causal analysis of interventions.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use BSTS when you have a continuous time series of at least 30 observations and need to separate its structural components, forecast future values with calibrated uncertainty, or estimate the causal effect of an intervention using a counterfactual approach. It is especially suited to settings where the number of candidate predictors is large relative to the series length, because the spike-and-slab prior handles variable selection automatically. BSTS assumes the components are additive; if multiplicative structure dominates, a log transformation should precede modelling. When using the CausalImpact framework for causal inference, the pre-intervention control period must be long enough for the model to learn the counterfactual reliably.
Strengths & limitations
- Decomposes a time series into interpretable additive components — trend, seasonality, and regression — with posterior uncertainty on each.
- Spike-and-slab prior performs automatic Bayesian variable selection from many candidate predictors, avoiding overfitting without manual stepwise procedures.
- Directly supports counterfactual causal inference (CausalImpact) by predicting what would have happened without an intervention.
- Does not require the normality assumption to hold; the Bayesian inference machinery remains valid even when distributional assumptions are approximate.
- Requires a minimum of approximately 30 time-series observations for reliable component separation and MCMC convergence.
- Computationally intensive compared to classical state-space or ARIMA approaches, because the full posterior must be sampled.
- Results depend on prior specifications; prior sensitivity analysis is mandatory, especially for short series where the prior can dominate.
- Causal conclusions from CausalImpact rest on the assumption of no unmeasured confounders influencing both the series and the intervention timing.
Frequently asked
What is the difference between BSTS and ARIMA?
ARIMA models a time series as a single autoregressive-moving-average process and produces point forecasts with confidence intervals. BSTS explicitly decomposes the series into interpretable components (trend, seasonality, regression) and estimates them within a full Bayesian framework, yielding posterior distributions rather than point estimates. BSTS also performs automatic variable selection via the spike-and-slab prior, which ARIMA does not do.
How does CausalImpact use BSTS?
CausalImpact fits a BSTS model on the pre-intervention period (using control series as regressors) to learn the counterfactual — what the series would have looked like without the intervention. It then extrapolates that counterfactual into the post-intervention window and compares it to the actual observed values. The difference, expressed as a posterior distribution, is the estimated causal impact. The key assumption is that no unobserved confounders changed at the intervention time.
What is a spike-and-slab prior?
A spike-and-slab prior places a probability mass (the 'spike') at exactly zero for each regression coefficient and a diffuse distribution (the 'slab') away from zero. The MCMC sampler estimates, for each predictor, the posterior probability of inclusion in the model. Predictors with high inclusion probability contribute meaningfully to the fit; those with low inclusion probability are effectively dropped. This performs variable selection automatically without a separate stepwise procedure.
How many observations are needed for BSTS?
The statwise registry sets the minimum at 30 observations. With fewer points the trend and seasonal components cannot be separated reliably and MCMC convergence becomes difficult. For CausalImpact specifically, the pre-intervention period should be substantially longer than the post-intervention window to give the model enough data to learn a reliable counterfactual.
Sources
- Scott, S. L. & Varian, H. R. (2014). Predicting the Present with Bayesian Structural Time Series. International Journal of Mathematical Modelling and Numerical Optimisation, 5(1/2), 4–23. DOI: 10.1504/IJMMNO.2014.059942 ↗
- Brodersen, K. H., Gallusser, F., Koehler, J., Remy, N. & Scott, S. L. (2015). Inferring Causal Impact Using Bayesian Structural Time-Series Models. Annals of Applied Statistics, 9(1), 247–274. DOI: 10.1214/14-AOAS788 ↗
How to cite this page
ScholarGate. (2026, June 1). Bayesian Structural Time Series Model. ScholarGate. https://scholargate.app/en/bayesian/bayesian-structural-time-series
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ARIMAEconometrics↔ compare
- Bayesian RegressionBayesian↔ compare
- Interrupted Time SeriesCausal inference↔ compare
- MCMCBayesian↔ compare
- State Space ModelEconometrics↔ compare