Bayesian structural time series

In particular, it can be used in order to assess how much different marketing campaigns have contributed to the change in web search volumes, product sales, brand popularity and other relevant indicators.

Difference-in-differences models[1] and interrupted time series designs[2] are alternatives to this approach.

"In contrast to classical difference-in-differences schemes, state-space models make it possible to (i) infer the temporal evolution of attributable impact, (ii) incorporate empirical priors on the parameters in a fully Bayesian treatment, and (iii) flexibly accommodate multiple sources of variation, including the time-varying influence of contemporaneous covariates, i.e., synthetic controls.

[1] A possible drawback of the model can be its relatively complicated mathematical underpinning and difficult implementation as a computer program.

However, the programming language R has ready-to-use packages for calculating the BSTS model,[3][4] which do not require strong mathematical background from a researcher.