Inferring Causal Direction Suppose I have time series data for two variables, X and Y. Assume that I am already convinced that there is a causal relationship between the two, but that I am unsure of the direction. Also assume that there will be a short time delay between cause and effect (here, short means at least an order of magnitude less than the time interval between consecutive data points). Are there any standard/established methods for inferring the direction of the causal effect?
Granger causality seems like a potentially relevant concept, but I have only just heard about that concept and I am uncertain.
$\textbf{Edit}$: I want to clarify the "Assume I am already convinced that there is a causal relationship between the two" portion of my question. Let me give an example:
Early in the COVID-19 pandemic local (to my area) health centers weren't giving out tests because there had been no reported COVID-19 cases in the area. I guess tests were wanted more badly elsewhere. Once they got a few obvious-enough cases (I think they were hospitalizations) there started to be more testing.
Now imagine $X$ is the rate of overall testing and $Y$ is the rate at which we get positive results. We can expect, based on policies like the one I just described, that $Y$ has an affect on $X$. But, we also expect that more testing will just find more cases, so $X$ has an affect on $Y$. The question is: how much each way?
This isn't really the application I'm interested in, but I think it basically illustrates what I mean. When I say I'm convinced, I don't necessarily mean convinced by statistics. There are some situations where some kind of causal relationship is a reasonable guess a priori.

It's tricky to answer this question because you'd have to be much clearer on what you mean by I am already convinced that there is a causal relationship between the two, but let's assume God came down to earth and told you that there is a causal relationship between A and B. In this case, because it's time-series data, if it's possible to identify which one happens before the other, we can say that the one who happened earlier caused the other, since cause always preceding effect in time is a fairly accepted assumption.
However, according to your description, it's possible that you can not identify which one happened first. Granger causality won't help you here, since it's not even able to identify a causal relationship. The causality in its name is pretty unfortunate, according to Granger himself.
Jonas Peters has done some work on this topic and I think a good reading for you is this paper of his: Detecting the direction of causal time series. They fit an autoregressive moving average model and investigate noise to identify ordering of the causal relationship.
