Bayesian Structural Time Series (BSTS)

Bayesian structural time series (BSTS) is a state-space model that decomposes a series into trend, seasonal and regression components and estimates them with Bayesian methods, often with spike-and-slab variable selection.

베이지안 구조 시계열(BSTS)은 시계열을 추세·계절·회귀 성분으로 분해하고 베이지안 방법으로 추정하는 상태공간 모형으로, 흔히 스파이크-앤-슬랩 변수선택을 함께 쓴다.

How do I forecast a time series or estimate the effect of an intervention with full uncertainty?

불확실성까지 포함하여 시계열을 예측하거나 개입 효과를 어떻게 추정하나요?

Bayesian structural time series decomposes a series into trend, seasonality and regression on control series, producing posterior forecasts with credible intervals. It fits forecasting and intervention analysis, where the pre-intervention model predicts a counterfactual for the post-intervention period.

When to use Bayesian Structural Time Series (BSTS)

• A single outcome series with trend and seasonal components
• Estimating the effect of a campaign or policy using untreated control series
• Wanting posterior credible intervals for forecasts

When to use something else

• Several treated and untreated units with panel data; use synthetic control or difference-in-differences
• Simple short-term forecasts without uncertainty modeling; use exponential smoothing

Assumptions and requirements

• Control series unaffected by the intervention
• Stable relationship between outcome and controls before the intervention
• Appropriate priors and state components
• Convergence of the MCMC sampler

What the analysis reports

• Decomposed trend and seasonal components
• Posterior inclusion probabilities of regressors
• Forecasts or counterfactual predictions with credible intervals
• Estimated absolute and relative effect with posterior probability

How to report it

The BSTS model estimated a relative effect of [value]% on [outcome] (95% credible interval [[value], [value]]), with a posterior probability of a causal effect of [value].

Related methods

• SARIMAX Model
• Synthetic Control Method
• Interrupted Time Series Analysis

Run Bayesian Structural Time Series (BSTS) on Quorant