Can patterns over time help to determine cause and effect relationships in climate models?

Observing climatological processes over time gives rise to a series of measurements indexed by time, a so called time-series. Imagine, we measure the temperature at some point on Earth every hour over the course of a year. The data will certainly indicate oscillatory behaviour - a temporal pattern- with a period of approximately 24 hours - the daily cycle. Or we could observe an oscillation that takes a full year to complete - the yearly cycle. By following a systematic procedure - the Fourier Transform - we get a description of the full time series as a superposition, or combination, of oscillations, each with a distinguished intensity and frequency.

So there are different angles from which we can look at a time-series. This might lead to the question whether changing the perspective on a time-series could reveal additional insights on the cause and effect relationships in a system of climatological processes. For instance, in addition to asking whether process A influences process B with a delay of 2 days, we could investigate, for example, to what extent the weekly oscillation of process A influences the 2-week oscillations of process B. Or to look at it in a different way, can we expect a change in the intensity of the 2-week cycle of process B if we were to manipulate the intensity of the weekly cycle of process A?

During my first project I am investigating how causal effect measures can be designed by bringing different time-series representations into the causal inference framework. Furthermore, I am trying to find convincing interpretations and sufficiently reliable statistical estimates for those quantities.