My data consists of a bunch of time series of daily clicks on some merchandises on a website, a portion of which have an intervention (only 1 intervention per time series), others don't. The intervention happens at different timing at different time series in the past. I want to measure the causal effect of the intervention on the treated group collectively (ideally with some confidence interval).
added sample data:
day item clicks timeperiod 1. 'A' 20. 'before intervention' 2. 'A' 18. 'before intervention' 3. 'A' 22. 'before intervention' ... 100. 'A' 26. 'after intervention' <-intervention event happened on day-100 101. 'A' 32. 'after intervention' 102. 'A' 30. 'after intervention' 103. 'A' 38. 'after intervention' 1. 'B' 30. 'before intervention' 2. 'B' 38. 'before intervention' 3. 'B' 32. 'before intervention' ... 50. 'B' 56. 'after intervention' <-intervention event happened on day-50 51. 'B' 52. 'after intervention' 52. 'B' 40. 'after intervention' 53. 'B' 58. 'after intervention' ...
And for items that did not receive the intervention, it's similar except the last col doesn't exist
I have some questions:
- How can I aggregate the treated time series despite the different timing of the interventions? Assuming there are other cofounders that make the traffic vary. I was trying to find some implementation to refer to but haven't found any yet.
- would it make sense to measure the effect on individual treated time series and report the distribution of effects instead? is it better to approach it at a collective level or individual level?
- When is it better to use matching vs synthetic data for choosing controls?
Thanks in advance for any answers!