Inspired by my 2025 data science internship | By Chris Oh

Most people think of time series analysis as forecasting – predicting what comes next. But forecasting isn’t the only thing we can do with time series data. We can also use it to answer a causal question: what was the effect of an intervention?

This is something that happened in the past, and is especially useful when experiments aren’t possible. Think of a Super Bowl ad, a global product launch, or a nationwide policy change. You can’t run an A/B test in those cases.

That’s where Bayesian Structural Time Series (BSTS) models come in.

What is a Time Series?

A time series is just data collected over time at regular intervals. Examples:

• Daily active users on your app
• Monthly sales revenue

What makes time series special is that each data point is not independent; today’s value is often influenced by yesterday’s. Time series analysis tries to capture these patterns: trend, seasonality, and noise.

Formally, a time series model can be written as:

$$ y_t = \mu_t + \tau_t + \beta X_t + \epsilon_t $$

Where:

• $y_t$: observed outcome at time $t$
• $\mu_t$: trend (long-term movements)
• $\tau_t$: seasonality (recurring cycles)
• $\beta X_t$: covariates (predictors unaffected by the intervention)
• $\epsilon_t$: random noise

This decomposition allows us to not just fit a line through the past, but to model the underlying structure of the system.

The Setup: Pre- and Post-Intervention

When measuring causal impact in time series, we split the data into two periods: