Statistics, experimentation, causal reasoning · insight-0026

Model seasonality explicitly in an interrupted time series or the season will pose as the effect

Situation
A new ancillary bundle launched in May, and a before/after regression on monthly revenue per passenger shows a jump.
Action
Use several full seasonal cycles before the intervention, add month terms, Fourier terms or splines, check residual autocorrelation, and compare with the same calendar months in earlier years. Report the effect with and without seasonal adjustment.
Reason
Segmented regression attributes any level or slope change at the break to the intervention; uneven seasonal composition around the break biases that attribution.
Boundary
Policy changes, product launches and pricing changes evaluated on a single aggregated series.

Symptom or risk

The post-period contains more peak months than the pre-period, so normal summer seasonality is credited to the launch.

Series without seasonality, or comparisons with a control series exposed to the same seasons, need less seasonal modelling.

More seasonal terms use degrees of freedom and widen intervals when the history is short.

Starting the pre-period at a seasonal trough to make the post-period look stronger.

In interrupted time series, seasonality can bias the estimate when pre- and post-intervention periods contain uneven seasonal months; it can be modelled with calendar-month terms, Fourier terms or splines, and residual autocorrelation should be checked.
Interrupted time series regression for the evaluation of public health interventions: a tutorial