# Causal inference on time-series data: is intervention needed?

I'm working on the topic of causal inference, I use time-series data. I have two scenarios in front of me and I don't understand the difference:

• Given X and Y "time" features. I would like to know whether X, e.g. average income, does it cause Y, e.g. hotel reservations.
• Given X "time" feature and an intervention. I'm curious to see how the intervention affects X. As an example, I publish a new web interface, while I look at the amount of purchases.

Are both causal inferences? What is the difference between them in practice? A good tool for the second is Google Causalimpact. Could you give me examples of the estimation methods in both cases?

Earlier, I used causal inference on cross-section data sets and that was obvious for me, because I could use DoWhy and a kind of matching and scoring-based estimation methods.

• Let's assume, there are seasons that make you adventurous. They lead to you earning more money but also and independently make you travel and book hotels. In that case earnings and bookings will be correlated but not because one is the cause of the other. So causality is difficult to establish. It may as well be, that when people earn much money they spend it on bookings. Now, if you randomly intervene you cannot say the same in the second case. Neither X nor any third influence can have any influence on your random intervention so if there is causality it can go in only one direction. Nov 18, 2023 at 8:58
• Thanks @Bernhard So are we talking about causal inference only in the second case? In the first case, we can only talk about correlation. And maybe the correlation can be used to create a causal graph.
– anon
Nov 18, 2023 at 9:17
• Both questions are questions of causal inference. Causal inference with interventional data is generally easier than with purely observational data, but that does not change the nature of the question. Nov 18, 2023 at 11:29
• I concur with @Scriddie . Both are causal questions but in the second case it is far easier to establish causality in comparison. In the first case, no statistical means can establish causality. Instead you need to include far more knowledge and assumptions from your expert knowledge. Nov 18, 2023 at 19:27

Both are identical problems. The purpose of intervention is the measure causal effect size between X and Y. For example if income is increased at some point in time, if the same unit (person or family) would consume more hotel reservation services. Such that, in do-calculus notation, $$P(Y|do(X))$$ provides a tool to impose intervention on X, i.e., increasing salary. This is so called Causal Discovery with Interventions